A371405 Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+3*x)^3 ) ).

1, 10, 136, 2134, 36379, 654670, 12239560, 235407070, 4627854244, 92576970280, 1878395043232, 38564373070090, 799651963174978, 16722655896174004, 352289843771100400, 7469327989417602862, 159263992188702829900, 3412969567344634872952

Offset: 0

Author

Seiichi Manyama, Mar 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A364923.

Programs

PARI

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

PARI

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

Formula

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