1,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 833.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 227, #16.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 226.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=binomial(n+3, 4)*binomial(n+3, 2)

G.f.: x*(6+8*x+x^2)/(1-x)^7.

E.g.f. with offset 3: exp(x)*(6*(x^3)/3! + 26*(x^4)/4! +35*(x^5)/5! + 15*(x^6)/6!). See row k=3 of A112486 for the coefficients [6, 26, 35, 15].

a(n)= (f(n+2, 3)/6!)*sum(A112486(3, m)*f(6, 3-m)*f(n-1, m), m=0..min(3, n)), with the falling factorials notation f(n, m):=n*(n-1)*...*(n-(m-1)).

a(n) = A000217 * n! / ( 4! * (n-4)! ) [for n>4 and A000217 = The Triangle Numbers], a(n) = ((n+4)! / n! ) ^2 / ( (n+2) * (n+1) * 2*4!), a(n) = (n-0)^2 * (n-1)^2 * (n-2) * (n-3) / (2*4!). - Jason Lang, Oct 03 2006

a(n)=numbperm (n,2)*numbperm (n,4)/48, n>=4 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007

a(n)=15*binomial(n+5,6)-10*binomial(n+4,5)+binomial(n+3,4). E.g.f. with offset 4: exp(x)*(1/4*x^4+1/6*x^5+1/48*x^6) - Miklos Kristof (kristmikl(AT)freemail.hu), Nov 04 2007

a(n) = n*(n+1)(n+2)^2*(n+3)^2/48 [From Jeremy Galvagni (jgalvagni(AT)mohawkteachers.org), Mar 03 2009]

seq(numbperm (n, 2)*numbperm (n, 4)/48, n=4..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007

a:=n->sum(sum(binomial(j, 1)*binomial(k, 3), j=0..n), k=0..n): seq(a(n), n=3..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007

seq(15*binomial(n+2, 6)-10*binomial(n+1, 5)+binomial(n, 4), n=4..30); - Miklos Kristof (kristmikl(AT)freemail.hu), Nov 04 2007

A001303:=-(6+8*z+z**2)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]

(Other) sage: [stirling_number1(n, n-3) for n in xrange(4, 34)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]

Sequence in context: A062801 A035290 A138422 this_sequence A027330 A090409 A039742

Adjacent sequences: A001300 A001301 A001302 this_sequence A001304 A001305 A001306

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000

Edited notation of the polynomial formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 15 2009