A053136 Binomial coefficients C(2*n+7,7).

1, 36, 330, 1716, 6435, 19448, 50388, 116280, 245157, 480700, 888030, 1560780, 2629575, 4272048, 6724520, 10295472, 15380937, 22481940, 32224114, 45379620, 62891499, 85900584, 115775100, 154143080, 202927725, 264385836, 341149446, 436270780, 553270671, 696190560

Offset: 0

Author

Wolfdieter Lang

Keywords

• nonn
• easy

Comments

Even-indexed members of eighth column of Pascal's triangle A007318.

Number of standard tableaux of shape (2n+1,1^7). - Emeric Deutsch, May 30 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Milan Janjić, Two Enumerative Functions.
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A007318, A053135, A000580, A053129.

Programs

Magma

[Binomial(2*n+7,7): n in [0..30]]; // Vincenzo Librandi, Oct 07 2011

Mathematica

Table[Binomial[2*n+7, 7], {n, 0, 30}] (* G. C. Greubel, Sep 03 2018 *)

PARI

a(n)=binomial(2*n+7,7) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = binomial(2*n+7, 7) = A000580(2*n+7).

G.f.: (1 + 28*x + 70*x^2 + 28*x^3 + x^4)/(1-x)^8.

E.g.f.: (630 + 22050*x + 81585*x^2 + 87465*x^3 + 36960*x^4 + 6888*x^5 + 560*x^6 + 16*x^7)*exp(x)/630. - G. C. Greubel, Sep 03 2018

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=0} 1/a(n) = 224*log(2) - 4627/30.

Sum_{n>=0} (-1)^n/a(n) = 28*log(2) - 553/30. (End)