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A369013
Expansion of (1/x) * Series_Reversion( x * (1-x^2/(1-x))^3 ).
5
1, 0, 3, 3, 27, 60, 355, 1128, 5694, 21610, 102462, 426465, 1978547, 8659386, 40003167, 180241995, 834994605, 3830870574, 17841265598, 82854767805, 388124777739, 1818343250570, 8565240659274, 40398758877564, 191254160050512, 906956708168838, 4312790630717025
OFFSET
0,3
COMMENTS
Satisfies a 7-term D-finite recurrence with 7-order polynomials. - R. J. Mathar, Jan 25 2024
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(n-k-1,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x^2/(1-x))^3)/x)
(PARI) a(n, s=2, t=3, u=-3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
Sequence in context: A157036 A080302 A080272 * A215829 A098340 A271938
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 11 2024
STATUS
approved