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A368971
Expansion of (1/x) * Series_Reversion( x * (1-x+x^2)^3 ).
2
1, 3, 12, 52, 228, 969, 3795, 12285, 19227, -162316, -2334219, -20233746, -146642814, -956899038, -5761740810, -32172133140, -164988072288, -752632536117, -2777949390584, -5070274066512, 41416739288496, 663038498204040, 6188361199762260, 47738255512890555
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n+k+2,k) * binomial(4*n-k+2,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x+x^2)^3)/x)
(PARI) a(n, s=2, t=3, u=0) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
Cf. A368963.
Sequence in context: A241468 A224914 A227810 * A362595 A125187 A151190
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 10 2024
STATUS
approved