A378613 a(n) = Sum_{k=0..n} binomial(4*n+k-1,k) * binomial(n-1,n-k).
1, 4, 44, 532, 6748, 88024, 1169444, 15738328, 213842716, 2927097712, 40302226944, 557565134196, 7744326799684, 107925260553088, 1508352084699224, 21132667178858512, 296716493251706652, 4174006026061733232, 58816013334014598032, 830025065117154066064, 11729345524163083673648
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*n+k-1, k)*binomial(n-1, n-k));
Formula
a(n) = [x^n] 1/(1 - x/(1 - x))^(4*n).
a(n) = (1/8)^n * [x^(4*n)] 4/(1 - x/(1 - x))^n for n > 0.