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Search: id:A090816
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| A090816 |
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a(n)=(3n+1)!/((2n)!n!). |
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+0
3
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| 1, 12, 105, 840, 6435, 48048, 352716, 2558160, 18386775, 131231100, 931395465, 6580248480, 46312074900, 324897017760, 2272989850440, 15863901576864, 110487596768703, 768095592509700, 5330949171823275, 36945070220658600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=1/(integral_{x=0 to 1}(x^2-x^3)^n dx).
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FORMULA
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a:=n->sum(j*binomial(n,j)*binomial(2*n-1,j),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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EXAMPLE
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E.g. a(3)=840.
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MAPLE
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a:=n->sum(j*binomial(n, j)*binomial(2*n-1, j), j=0..n): seq(a(n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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MATHEMATICA
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f[n_] := 1/Integrate[(x^2 - x^3)^n, {x, 0, 1}]; Table[ f[n], {n, 0, 19}] (from Robert G. Wilson v Feb 18 2004)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (3*n+1)!/(2*n)!/n!) - Michael Somos Feb 14 2004
(PARI) a(n)=if(n<0, 0, 1/subst(intformal((x^2-x^3)^n), x, 1)) - Michael Somos Feb 14 2004
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CROSSREFS
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Cf. A045721.
Halfdiagonal of triangle A003506.
Sequence in context: A004321 A016223 A027142 this_sequence A144133 A089396 A166755
Adjacent sequences: A090813 A090814 A090815 this_sequence A090817 A090818 A090819
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Feb 11 2004
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EXTENSIONS
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New definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 12 2004
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