|
|
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, 436270780, 553270671, 696190560
(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
|
|
|
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
Sum_{n>=0} 1/a(n) = 224*log(2) - 4627/30.
Sum_{n>=0} (-1)^n/a(n) = 28*log(2) - 553/30. (End)
|
|
MATHEMATICA
|
Table[Binomial[2*n+7, 7], {n, 0, 30}] (* G. C. Greubel, Sep 03 2018 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|