A360990 E.g.f. satisfies A(x) = exp(x / A(-x)^3).

1, 1, 7, -8, -827, 2896, 452179, -2511872, -560237303, 4254259456, 1237434920191, -11907540107264, -4275828959720435, 49800209789734912, 21288959122755516235, -290981680034059649024, -144324916601232035246831, 2264121148389579474141184

Offset: 0

Author

Seiichi Manyama, Feb 27 2023

Keywords

• sign

Crossrefs

Cf. A141369, A196198, A360987, A360988, A360989.

Programs

Maple

A360990 := proc(n)
    add((-3*n+3*k+1)^(k-1)*(3*k)^(n-k)*binomial(n,k),k=0..n) ;
end proc:
seq(A360990(n),n=0..60) ; # R. J. Mathar, Mar 12 2023

PARI

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

Formula

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