A034264 a(n) = f(n,4) where f is given in A034261.

0, 1, 11, 56, 196, 546, 1302, 2772, 5412, 9867, 17017, 28028, 44408, 68068, 101388, 147288, 209304, 291669, 399399, 538384, 715484, 938630, 1216930, 1560780, 1981980, 2493855, 3111381, 3851316, 4732336, 5775176, 7002776, 8440432

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A034261.

Programs

Maple

A034261 := proc(n, k) binomial(n+k, k+1)*(n*k+n+1)/(k+2); end;
seq( A034261(n,4),n=0..40) ;

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,11,56,196,546,1302},40] (* Harvey P. Dale, Jul 11 2025 *)

Formula

G.f.: -x*(1+4*x)/(x-1)^7. - R. J. Mathar, Feb 10 2025

a(n) = n*(5*n+1)*(n+4)*(n+3)*(n+2)*(n+1)/720. - R. J. Mathar, Feb 10 2025

Extensions

Corrected and extended by N. J. A. Sloane, Apr 21 2000