A105940 a(n) = binomial(n+5, 5)*binomial(n+8, 5).

56, 756, 5292, 25872, 99792, 324324, 924924, 2378376, 5621616, 12388376, 25729704, 50791104, 95938752, 174350232, 306211752, 521694096, 864913896, 1399125420, 2213431220, 3431347920, 5221616400, 7811703900, 11504509380, 16698853080, 23914406880, 33821804016

Offset: 0

Author

Zerinvary Lajos, Apr 27 2005

Keywords

• easy
• nonn

Examples

			a(0) = C(0+5,0)*C(0+8,5) = C(5,0)*C(8,5) = 1*56 = 56
a(6) = C(6+5,6)*C(6+8,5) = C(11,6)*C(14,5) = 462*2002 = 924924.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A062145.

Programs

Magma

A105940:= func< n | Binomial(n+5,5)*Binomial(n+8,5) >;
[A105940(n): n in [0..40]]; // G. C. Greubel, Mar 11 2025

Maple

with(combinat); for i from 0 to 25 do print(i,numbcomb(i+5,i)*numbcomb(i+8,5)); end; # Jim Nastos, Oct 26 2005

Mathematica

a[n_] := Binomial[n + 5, 5] * Binomial[n + 8, 5]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

SageMath

def A105940(n): return binomial(n+5,5)*binomial(n+8,5)
print([A105940(n) for n in range(41)]) # G. C. Greubel, Mar 11 2025

Formula

G.f.: 28*(2+x)*(1+2*x) / (1-x)^11. - Colin Barker, Jan 28 2013

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 580367/1764 - 100*Pi^2/3.

Sum_{n>=0} (-1)^n/a(n) = 74537/588 - 1280*log(2)/7. (End)

Extensions

More terms from Jim Nastos, Oct 26 2005