A366114 Expansion of (1/x) * Series_Reversion( x*(1+x+x^2)/(1+x)^3 ).

1, 2, 4, 7, 9, 2, -34, -130, -284, -284, 730, 4864, 14860, 27134, 6462, -170865, -771303, -2005828, -2751028, 3491747, 36288137, 130265102, 283131062, 210905402, -1317613954, -7461822262, -22297519418, -38398674146, 10151248222, 355843715494, 1495838414326

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(2*n-k+2, n-2*k))/(n+1);

Crossrefs

Cf. A127632, A364374, A366115.

Cf. A279565.

Sequence in context: A094446 A370003 A071790 * A199465 A288305 A081249

Adjacent sequences: A366111 A366112 A366113 * A366115 A366116 A366117

Keyword

sign

Author

Seiichi Manyama, Sep 29 2023

Status

approved