A105250 a(n) = binomial(n+3,n)*binomial(n+7,n).

1, 32, 360, 2400, 11550, 44352, 144144, 411840, 1061775, 2516800, 5562128, 11583936, 22926540, 43411200, 79070400, 139163904, 237557133, 394558560, 639331000, 1013012000, 1572701130, 2396496960, 3589794000, 5293080000, 7691506875, 11026544256, 15610063392

Offset: 0

Author

Zerinvary Lajos, Apr 14 2005

Keywords

• easy
• nonn

Examples

			a(0): C(0+3,0)*C(0+7,0) = C(3,0)*C(7,0) = 1*1 = 1;
a(10): C(10+3,10)*C(10+7,10) = C(13,10)*(17,10) = 286*19448 = 5562128.
		

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. A062264.

Programs

Magma

[Binomial(n+3,n)*Binomial(n+7,n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Mathematica

f[n_] := Binomial[n + 3, n]Binomial[n + 7, n]; Table[ f[n], {n, 0, 23}] (* Robert G. Wilson v, Apr 20 2005 *)

SageMath

def A105250(n): return binomial(n+3,n)*binomial(n+7,n)
print([A105250(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Formula

G.f.: (1+21*x+63*x^2+35*x^3)/(1-x)^11. - Colin Barker, Jan 21 2013

a(n) = 11*a(n-1) -55*a(n-2) +165*a(n-3) -330*a(n-4) +462*a(n-5) -462*a(n-6) +330*a(n-7) -165*a(n-8) +55*a(n-9) -11*a(n-10) +a(n-11). - Wesley Ivan Hurt, May 24 2021

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 98*Pi^2 - 72464/75.

Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2 + 1792*log(2)/5 - 15827/50. (End)

Extensions

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