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A377197
Expansion of 1/(1 - 4*x/(1-x))^(3/2).
5
1, 6, 36, 206, 1146, 6258, 33728, 180018, 953628, 5021698, 26315676, 137350746, 714455826, 3705635646, 19171860336, 98973407550, 509963556330, 2623133951730, 13472299015580, 69098721151530, 353966981339070, 1811212435206070, 9258333786967920, 47281424213258070
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (3-k/n) * a(k).
a(n) = (6*n*a(n-1) - 5*(n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (2*k+1) * binomial(2*k,k) * binomial(n-1,n-k).
a(n) ~ 16 * sqrt(n) * 5^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Oct 26 2024
PROG
(PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(2*k, k)*binomial(n-1, n-k));
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, Oct 19 2024
STATUS
approved