A368961 Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^2 ).

1, 2, 9, 48, 286, 1820, 12116, 83334, 587537, 4223582, 30840355, 228111390, 1705509981, 12868775056, 97867753424, 749401318160, 5772939358590, 44708058004740, 347879528717526, 2718400037837988, 21323471768334120, 167844335760482220, 1325332432687278960

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(3*n-k+1,n-2*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^2)/x)
(PARI) a(n, s=2, t=2, u=0) = 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

Cf. A368965, A368967.

Cf. A001002.

Sequence in context: A118341 A365133 A171803 * A100427 A214404 A074143

Adjacent sequences: A368958 A368959 A368960 * A368962 A368963 A368964

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved