A104680 a(n) = binomial(n+7,7)*binomial(n+12,7).

792, 13728, 123552, 772200, 3775200, 15402816, 54609984, 172931616, 498841200, 1330243200, 3316739712, 7801876368, 17439488352, 37263864000, 76488984000, 151448188320, 290275694280, 540192201120, 978609060000, 1729734435000, 2988981103680, 5058275713920

Offset

0,1

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003, 1365,-455,105,-15,1).

Formula

G.f.: -264*(3+7*x+3*x^2)/(x-1)^15. - R. J. Mathar, Nov 29 2015

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 1263966463/1306800 - 98*Pi^2.

Sum_{n>=0} (-1)^n/a(n) = 3935051/13068 - 14336*log(2)/33. (End)

Example

If n=0 then C(0+7,0+0)*C(0+12,7) = C(7,0)*C(12,7) = 1*792 = 792.
If n=6 then C(6+7,6+0)*C(6+12,7) = C(13,6)*C(18,7) = 1716*32824 = 54609984.

Mathematica

a[n_] := Binomial[n + 7, 7] * Binomial[n + 12, 7]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)

Crossrefs

Cf. A062190.

Sequence in context: A104398 A186057 A027817 * A037190 A209893 A184491

Adjacent sequences: A104677 A104678 A104679 * A104681 A104682 A104683

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 22 2005

Status

approved