A380094 E.g.f. A(x) satisfies A(x) = ( 1 + 3*x*exp(x*A(x)) )^(1/3).

1, 1, 0, 7, -28, 405, -4514, 75313, -1336824, 28494793, -672782950, 17874984501, -521966931716, 16702822898749, -579928752836874, 21736834275178345, -874384126286848624, 37581186999500130321, -1718628399364227445070, 83327485224351815544925

Offset: 0

Author

Seiichi Manyama, Jan 12 2025

Keywords

• sign

Crossrefs

Cf. A161631, A380093.

Cf. A380051.

Programs

PARI

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

Formula

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