A369076 Expansion of (1/x) * Series_Reversion( x * (1+x^2/(1-x))^2 ).

1, 0, -2, -2, 9, 24, -37, -240, -2, 2126, 2919, -16052, -50663, 86940, 631995, 19094, -6491463, -9595434, 54443985, 181532910, -317331187, -2426618056, -133151895, 26332109928, 40544827703, -230619508548, -793966990358, 1384746844832, 10960715925621, 881359815524

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1+x^2/(1-x))^2)/x)
(PARI) a(n, s=2, t=2, u=-2) = 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. A168491, A369077.

Cf. A368969, A368973, A368975.

Cf. A368957.

Sequence in context: A220971 A368182 A363451 * A308519 A205390 A204265

Adjacent sequences: A369073 A369074 A369075 * A369077 A369078 A369079

Keyword

sign

Author

Seiichi Manyama, Jan 12 2024

Status

approved