A365177 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^3).

1, 1, 10, 201, 6220, 261465, 13925286, 898994383, 68240292856, 5956670911041, 587896878021130, 64738492669538391, 7869297152389747284, 1046629627952327990545, 151192146681811716344878, 23573456446401808474471455, 3945806733850334447131941616

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A364987, A364989, A365175, A365176.

Sequence in context: A210168 A041180 A367200 * A027014 A088746 A293970

Adjacent sequences: A365174 A365175 A365176 * A365178 A365179 A365180

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved