A104673 a(n) = binomial(n+5, n)*binomial(n+10, n).

1, 66, 1386, 16016, 126126, 756756, 3699696, 15402816, 56316546, 184940756, 554822268, 1540663488, 4001445448, 9802357488, 22805484768, 50678855040, 108088495515, 222161129190, 441579528390, 851355545040, 1596291646950, 2917485413700, 5208073135200

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: (1 + 50*x + 450*x^2 + 1200*x^3 + 1050*x^4 + 252*x^5)/(1-x)^16. - Harvey P. Dale, Nov 24 2011

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 17875*Pi^2/3 - 7468753315/127008.

Sum_{n>=0} (-1)^n/a(n) = 208828891/127008 - 725*Pi^2/6 - 40960*log(2)/63. (End)

Example

If n=0 then C(0+5,5)*C(0+10,0+0) = C(5,5)*C(10,0) = 1*1 = 1.
If n=6 then C(6+5,5)*C(6+10,6+0) = C(11,5)*C(16,6) = 462*8008 = 3699696.

Mathematica

Table[Binomial[n+5, 5]Binomial[n+10, n], {n, 0, 30}]

Prog

(Magma)
A104673:= func< n | Binomial(n+5, n)*Binomial(n+10, n) >;
[A104673(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025
(SageMath)
def A104673(n): return binomial(n+5, n)*binomial(n+10, n)
print([A104673(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025

Crossrefs

Cf. A062190.

Sequence in context: A263522 A269693 A278850 * A251047 A279889 A241799

Adjacent sequences: A104670 A104671 A104672 * A104674 A104675 A104676

Keyword

easy,nonn,changed

Author

Zerinvary Lajos, Apr 22 2005

Extensions

Corrected and extended by Harvey P. Dale, Nov 24 2011

Status

approved