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Search: id:A033487
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| A033487 |
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n*(n+1)*(n+2)*(n+3)/4. |
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+0
10
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| 0, 6, 30, 90, 210, 420, 756, 1260, 1980, 2970, 4290, 6006, 8190, 10920, 14280, 18360, 23256, 29070, 35910, 43890, 53130, 63756, 75900, 89700, 105300, 122850, 142506, 164430, 188790, 215760, 245520, 278256, 314160, 353430, 396270, 442890, 493506
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
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LINKS
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Index entries for sequences related to Bessel functions or polynomials
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FORMULA
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G.f.: -6*x/(x-1)^5. a(n)=6*C(n+3, 4)=a(n-1)+A007531(n+1)=6*A000332(n)=sum_{i = 0 to n} (i*(i+1)*(i+2)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 10 2001
Constant term in Bessel polynomial {y_n(x)}''.
(Binomial(n+2,n)*binomial(n+2,n)-binomial(n+2,n) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2006
a(n)=(sum(sum((i*j), i=2.. n), j=1..n)), n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
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MAPLE
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[seq(binomial(n, 4)*6, n=3..40)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 18 2006
a:=n->(sum(sum((i*j), i=2.. n), j=1..n)):seq(a(n), n=1..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
a:=n->add(binomial(n, 2)+add(binomial(n, 2), j=0..n), j=0..n):seq(a(n)/2, n=1..30); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
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MATHEMATICA
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f[n_]:=n*(n+1)*(n+2)*(n+3)/4; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
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CROSSREFS
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Partial sums of A007531.
Cf. A050534, A034827.
A033486, A033488 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
Sequence in context: A009775 A119536 A107394 this_sequence A061138 A073948 A101855
Adjacent sequences: A033484 A033485 A033486 this_sequence A033488 A033489 A033490
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 18 2006
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