A371407 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+3*x)^2 ) ).

1, 8, 86, 1064, 14289, 202488, 2980380, 45122792, 698214548, 10993069856, 175546104958, 2836384141720, 46285381498750, 761735217877200, 12628402069223160, 210704642400488040, 3535494883741420908, 59621314428576557664, 1009942893735988354296

Offset: 0

Author

Seiichi Manyama, Mar 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A002293, A371406.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+3*x)^2))/x)

PARI

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

Formula

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