A371432 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2 + x^4) ).

1, 2, 7, 30, 142, 714, 3740, 20178, 111325, 625042, 3559101, 20502014, 119249277, 699330360, 4130235408, 24543145310, 146629131642, 880184547880, 5305961255490, 32107022363150, 194947974895960, 1187354222296110, 7252099548616320, 44408257163905050

Offset: 0

Author

Seiichi Manyama, Mar 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369124, A371435.

Cf. A369160.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2+x^4))/x)

PARI

a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+k,k) * binomial(3*n-2*k+1,n-4*k).