A380096 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*A(x)^3*exp(x*A(x)^3) )^(1/3).

1, 1, 12, 289, 10724, 540745, 34551886, 2676439507, 243782162408, 25535467766593, 3024360522754010, 399665508962874451, 58301379215119084012, 9305724270031402836337, 1613262216112899513140630, 301870732625016111841693795, 60639884085040694650040518736

Offset

0,3

Links

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

Formula

E.g.f.: ( (1/x) * Series_Reversion(x*(1 - 3*x*exp(x))) )^(1/3).

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

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

Prog

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

Crossrefs

Cf. A213644, A380095.

Cf. A380043, A380097.

Sequence in context: A226100 A041267 A041264 * A220307 A361302 A361309

Adjacent sequences: A380093 A380094 A380095 * A380097 A380109 A380113

Keyword

nonn,new

Author

Seiichi Manyama, Jan 12 2025

Status

approved