A370107 Expansion of (1/x) * Series_Reversion( x / ((1-x)^2 * (1+x)^3) ).

1, 1, -1, -7, -10, 27, 152, 169, -949, -4286, -2646, 36499, 133684, -376, -1458768, -4325495, 3422105, 59242995, 139491393, -260949134, -2414487452, -4307455022, 15274866472, 97910544003, 119082795965, -805538039024, -3921641157424, -2408010178616, 40104318820288

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Index entries for reversions of series

Formula

G.f.: exp( Sum_{k>=1} A370106(k) * x^k/k ).

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

a(n) = (1/(n+1)) * [x^n] ( (1-x)^2 * (1+x)^3 )^(n+1).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);
(PARI) my(x='x+O('x^30)); Vec(serreverse(x/((1-x)^2*(1+x)^3))/x) \\ Michel Marcus, Feb 10 2024

Crossrefs

Cf. A291534, A369190.

Cf. A370106.

Sequence in context: A064950 A240795 A058532 * A280966 A360430 A174466

Adjacent sequences: A370104 A370105 A370106 * A370108 A370109 A370110

Keyword

sign

Author

Seiichi Manyama, Feb 10 2024

Status

approved