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A377216
Expansion of 1/(1 - 4*x^3/(1-x))^(5/2).
2
1, 0, 0, 10, 10, 10, 80, 150, 220, 710, 1620, 2950, 7010, 16110, 32560, 70682, 156810, 329290, 698540, 1507110, 3189742, 6725150, 14279520, 30141730, 63335960, 133297362, 279996460, 586364410, 1227337710, 2566307410, 5355970048, 11166535430, 23259949980, 48389451510
OFFSET
0,4
FORMULA
a(n) = (2*(n-1)*a(n-1) - (n-2)*a(n-2) + 2*(2*n+9)*a(n-3) - 2*(2*n+2)*a(n-4))/n for n > 3.
a(n) = Sum_{k=0..floor(n/3)} (-4)^k * binomial(-5/2,k) * binomial(n-2*k-1,n-3*k).
PROG
(PARI) a(n) = sum(k=0, n\3, (-4)^k*binomial(-5/2, k)*binomial(n-2*k-1, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 20 2024
STATUS
approved