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A053136 Binomial coefficients C(2*n+7,7). 5

%I

%S 1,36,330,1716,6435,19448,50388,116280,245157,480700,888030,1560780,

%T 2629575,4272048,6724520,10295472,15380937,22481940,32224114,45379620,

%U 62891499,85900584,115775100,154143080,202927725,264385836,341149446

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

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

%C Number of standard tableaux of shape (2n+1,1^7) - _Emeric Deutsch_, May 30 2004

%H Vincenzo Librandi, <a href="/A053136/b053136.txt">Table of n, a(n) for n = 0..200</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).

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

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

%F 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

%t Table[Binomial[2*n+7, 7], {n, 0, 30}] (* _G. C. Greubel_, Sep 03 2018 *)

%o (MAGMA)[Binomial(2*n+7,7): n in [0..30]]; // _Vincenzo Librandi_, Oct 07 2011

%o (PARI) a(n)=binomial(2*n+7,7) \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A053135, A000580, A053129.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)