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A377199
Expansion of 1/(1 - 4*x/(1-x))^(5/2).
4
1, 10, 80, 570, 3790, 24062, 147780, 885190, 5199560, 30065870, 171623328, 969151710, 5422863630, 30105497970, 165993714540, 909770119914, 4959840748350, 26912374137150, 145411035749600, 782681600883950, 4198276264607290, 22448626776903450, 119690255236279100
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (5-3*k/n) * a(k).
a(n) = (2*(3*n+2)*a(n-1) - 5*(n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(n-1,n-k).
a(n) ~ 128 * n^(3/2) * 5^(n - 5/2) / (3*sqrt(Pi)). - Vaclav Kotesovec, Oct 26 2024
PROG
(PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(n-1, n-k));
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Seiichi Manyama, Oct 19 2024
STATUS
approved