A368938 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^2) ).

1, 3, 14, 78, 479, 3129, 21332, 150057, 1081118, 7937589, 59174752, 446744610, 3408616155, 26242751046, 203615759472, 1590550846398, 12498584431503, 98731454253945, 783581338236326, 6245066800130298, 49961547869830135, 401076129627216180, 3229808459696023980

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-2*k).

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-2*k))/(n+1);
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x+x^2))/x)

Crossrefs

Cf. A129442, A368934.

Sequence in context: A074538 A364739 A366083 * A242426 A001564 A277132

Adjacent sequences: A368935 A368936 A368937 * A368939 A368940 A368941

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved