A104671 a(n) = C(n+3,3)*C(n+8,n+0).

1, 36, 450, 3300, 17325, 72072, 252252, 772200, 2123550, 5348200, 12514788, 27511848, 57316350, 113954400, 217443600, 400096224, 712671399, 1232995500, 2077825750, 3418915500, 5504453955, 8687301480, 13461727500, 20510685000, 30766027500, 45484495056

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12. - Bruno Berselli, Jun 06 2012

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 144*Pi^2 - 1739736/1225.

Sum_{n>=0} (-1)^n/a(n) = 16*Pi^2 - 13312*log(2)/35 - 515202/1225. (End)

Example

If n=0 then C(0+3,3)*C(0+8,0+0)= C(3,3)*C(8,0)=1*1=1
If n=6 then C(6+3,3)*C(6+8,6+0)= C(9,3)*C(14,6)=84*3003=252252

Mathematica

Table[Binomial[n+3, 3]Binomial[n+8, n], {n, 0, 30}] (* or *) LinearRecurrence[ {12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {1, 36, 450, 3300, 17325, 72072, 252252, 772200, 2123550, 5348200, 12514788, 27511848}, 30] (* Harvey P. Dale, Oct 05 2017 *)

Crossrefs

Cf. A062190.

Sequence in context: A256149 A244498 A110693 * A323549 A128986 A281371

Adjacent sequences: A104668 A104669 A104670 * A104672 A104673 A104674

Keyword

nonn,easy

Author

Zerinvary Lajos, Apr 22 2005

Extensions

a(12) corrected by Colin Barker, Jun 06 2012

More terms and a(7), a(15) corrected by Bruno Berselli, Jun 06 2012

Status

approved