1,1

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, December 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

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.]

Adjacent sequences: A001300 A001301 A001302 this_sequence A001304 A001305 A001306

Sequence in context: A062801 A035290 A138422 this_sequence A027330 A090409 A039742

nonn

njas

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