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

Author

Zerinvary Lajos, Apr 14 2005

Keywords

• easy
• nonn

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• 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).

Crossrefs

Cf. A062264.

Programs

Magma

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

Mathematica

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

SageMath

def A105254(n): return binomial(n+7,n)*binomial(n+11,n)
print([A105254(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Formula

G.f.: (1 + 77*x + 1155*x^2 + 5775*x^3 + 11550*x^4 + 9702*x^5 + 3234*x^6 + 330*x^7)/(1-x)^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)

Extensions

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

More terms from Colin Barker, Jan 21 2013