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A053136 Binomial coefficients C(2*n+7,7). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 Janjic, Two Enumerative Functions

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A053135, A000580, A053129.

Sequence in context: A223299 A068075 A219004 * A000821 A250422 A223307

Adjacent sequences:  A053133 A053134 A053135 * A053137 A053138 A053139

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)