A369161 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^4) ).

1, 3, 15, 91, 613, 4410, 33190, 258129, 2058281, 16737259, 138268611, 1157197639, 9790774861, 83606543660, 719638883748, 6237175439640, 54386540912490, 476782443732437, 4199713449255749, 37151346765537606, 329914740292813170, 2939975733035070000

Offset: 0

Author

Seiichi Manyama, Jan 15 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A063021, A369102, A369160.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^4))/x)

PARI

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

Formula

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