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A369402
Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3)^3 ).
2
1, 2, 5, 17, 72, 330, 1554, 7490, 36992, 186582, 956573, 4967425, 26070960, 138081690, 737120376, 3962039625, 21424392088, 116467354320, 636141911420, 3489357591052, 19213097243736, 106158276425242, 588409936029990, 3270832234633026, 18229957695363048
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(2*n+2,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 16 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^2*(1-x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
CROSSREFS
Sequence in context: A336282 A082282 A005967 * A104859 A108289 A007779
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 22 2024
STATUS
approved