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A214400
a(n) = binomial(n^2 + 3*n, n).
2
1, 4, 45, 816, 20475, 658008, 25827165, 1198774720, 64276915527, 3911395881900, 266401260897200, 20082459351180240, 1660305826125766950, 149389005978091284720, 14533945899753270066525, 1520398315196482557890304, 170190601112537814791748255
OFFSET
0,2
COMMENTS
Equals the central terms of triangle A214398.
LINKS
FORMULA
a(n) = [x^n] 1/(1 - x)^((n+1)^2). - Ilya Gutkovskiy, Oct 04 2017
a(n) ~ n^(n-1/2)*exp(n+5/2)/sqrt(2*Pi). - Robert Israel, Mar 04 2022
MAPLE
seq(binomial(n^2+3*n, n), n=0..30); # Robert Israel, Mar 04 2022
PROG
(PARI) a(n)=binomial(n^2+3*n, n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 15 2012
STATUS
approved