A105254 a(n) = binomial(n+7,n)*binomial(n+11,n).

1, 96, 2808, 43680, 450450, 3459456, 21237216, 109219968, 486370170, 1921462400, 6859620768, 22449667968, 68128506264, 193501082880, 518306472000, 1317650231040, 3196331224515, 7432299594720, 16630917303000, 35933837940000, 75191555889450, 152770145299200

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).

Formula

G.f.: -(330*x^7+3234*x^6+9702*x^5+11550*x^4+5775*x^3+1155*x^2+77*x+1)/(x-1)^19. - Colin Barker, Jan 21 2013

From Amiram Eldar, Sep 04 2022: (Start)

Sum_{n>=0} 1/a(n) = 308308*Pi^2/3 - 16431524791/16200.

Sum_{n>=0} (-1)^n/a(n) = 1232*Pi^2/3 + 360448*log(2)/45 - 108911693/11340. (End)

Example

a(0): C(0+7,0)*C(0+11,0) = C(7,0)*C(11,0) = 1*1 = 1;
a(8): C(8+7,8)*C(8+11,8) = C(15,8)*(19,8) = 6435*75582 = 486370170.

Mathematica

f[n_] := Binomial[n + 7, n]Binomial[n + 11, n]; Table[ f[n], {n, 0, 19}] (* Robert G. Wilson v, Apr 20 2005 *)

Prog

(Magma) [Binomial(n+7, n)*Binomial(n+11, n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Crossrefs

Sequence in context: A233709 A268901 A239158 * A234075 A347753 A164762

Adjacent sequences: A105251 A105252 A105253 * A105255 A105256 A105257

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 14 2005

Extensions

More terms from Robert G. Wilson v, Apr 20 2005

More terms from Colin Barker, Jan 21 2013

Status

approved