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A377215
Expansion of 1/(1 - 4*x^2/(1-x))^(5/2).
2
1, 0, 10, 10, 80, 150, 640, 1550, 5190, 13870, 41912, 115650, 333490, 925970, 2607540, 7220062, 20053700, 55230870, 152005380, 416295350, 1137980678, 3100453710, 8429823180, 22862244210, 61882724100, 167159512794, 450739897980, 1213298505770, 3260824389510
OFFSET
0,3
FORMULA
a(n) = (2*(n-1)*a(n-1) + (3*n+14)*a(n-2) - 2*(2*n-1)*a(n-3))/n for n > 2.
a(n) = Sum_{k=0..floor(n/2)} (-4)^k * binomial(-5/2,k) * binomial(n-k-1,n-2*k).
PROG
(PARI) a(n) = sum(k=0, n\2, (-4)^k*binomial(-5/2, k)*binomial(n-k-1, n-2*k));
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, Oct 20 2024
STATUS
approved