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A369403
Expansion of (1/x) * Series_Reversion( x / (1+x)^3 * (1-x^3)^3 ).
2
1, 3, 12, 58, 318, 1887, 11775, 76041, 503607, 3401326, 23337339, 162214074, 1139835938, 8083530360, 57783277608, 415904602938, 3011669994078, 21924967877547, 160374157346266, 1178091991206162, 8687419007293458, 64285383562018856, 477208235856114384
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(3*n+3,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 / (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)^3*(1-x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=3) = 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: A369616 A372378 A369594 * A291488 A090363 A115086
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 22 2024
STATUS
approved