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

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

Prog

(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);

Crossrefs

Cf. A364923.

Sequence in context: A129803 A065024 A026244 * A261503 A096619 A276131

Adjacent sequences: A371402 A371403 A371404 * A371406 A371407 A371408

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved