A369160 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^4) ).

1, 2, 7, 30, 144, 742, 4012, 22458, 129035, 756602, 4509141, 27233726, 166320987, 1025356360, 6372494608, 39882831334, 251146002084, 1590079213920, 10115878798130, 64634124182670, 414578955678690, 2668578654593970, 17232252926468640, 111602332042716450

Offset: 0

Author

Seiichi Manyama, Jan 15 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A063021, A369102, A369161.

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, 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)} binomial(n+k,k) * binomial(3*n-2*k+1,n-4*k).