A379909 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x).

1, 0, 1, -4, 41, -456, 6817, -120044, 2497105, -59445136, 1599030881, -47923901268, 1584315183673, -57269439049304, 2247345360390145, -95147690776024636, 4323183446836151201, -209835113176652954400, 10835768876261196612673, -593183387438256595660964

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = -n! * Sum_{k=0..n} (-2*n+2*k-1)^(n-k-1) * binomial(2*n-k,k)/(n-k)!.

Prog

(PARI) a(n) = -n!*sum(k=0, n, (-2*n+2*k-1)^(n-k-1)*binomial(2*n-k, k)/(n-k)!);

Crossrefs

Cf. A379856, A379868, A379877.

Sequence in context: A227996 A236528 A114467 * A118450 A024383 A110041

Adjacent sequences: A379906 A379907 A379908 * A379910 A379911 A379912

Keyword

sign

Author

Seiichi Manyama, Jan 05 2025

Status

approved