A105946 a(n) = C(n+3,3) * C(n+5,5).

1, 24, 210, 1120, 4410, 14112, 38808, 95040, 212355, 440440, 858858, 1589952, 2815540, 4798080, 7907040, 12651264, 19718181, 30020760, 44753170, 65456160, 94093230, 133138720, 185679000, 255528000, 347358375, 466849656, 620854794, 817586560, 1066825320

Offset: 0

Author

Zerinvary Lajos, Apr 27 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+5,0)*C(0+3,3) = C(5,0)*C(3,3) = 1*1 = 1.
If n=15 then C(15+5,15)*C(15+3,3) = C(20,15)*C(18,3) = 15504*816 = 12651264.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A062196.

Programs

Magma

A105946:= func< n | Binomial(n+3,3)*Binomial(n+5,5) >;
[A105946(n): n in [0..40]]; // G. C. Greubel, Feb 22 2025

Maple

A105946:=n->binomial(n+5,n)*binomial(n+3,3); seq(A105946(n), n=0..100); # Wesley Ivan Hurt, Nov 26 2013

Mathematica

Table[Binomial[n+5,n]*Binomial[n+3,3], {n,0,100}] (* Wesley Ivan Hurt, Nov 26 2013 *)

SageMath

def A105946(n): return binomial(n+3,3)*binomial(n+5,5)
print([A105946(n) for n in range(41)]) # G. C. Greubel, Feb 22 2025

Formula

G.f.: (1 + 15*x + 30*x^2 + 10*x^3)/(1-x)^9. - Colin Barker, Jan 28 2013

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 75*Pi^2/2 - 5905/16.

Sum_{n>=0} (-1)^n/a(n) = 160*log(2) - 5*Pi^2/4 - 4685/48. (End)

E.g.f.: (1/6!)*(720 + 16560*x + 58680*x^2 + 67320*x^3 + 32850*x^4 + 7686*x^5 + 893*x^6 + 49*x^7 + x^8)*exp(x). - G. C. Greubel, Feb 22 2025

Extensions

More terms from Colin Barker, Jan 28 2013