A371362 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1-2*x) ).

1, 4, 31, 298, 3199, 36742, 441748, 5489554, 69945295, 908836768, 11996580199, 160418984656, 2168512922692, 29584600414168, 406823494817560, 5632906243123090, 78465351036084655, 1098851032467132484, 15461857967408794333, 218490450548650811914

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A007564, A371363.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^2/(1-2*x))/x)

PARI

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

Formula

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