A379856 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x.

1, 0, 1, -7, 81, -1181, 21373, -462267, 11663137, -336711385, 10955316501, -396815693759, 15840688752529, -691086583866069, 32717602050027469, -1670649590632148611, 91530694441643402817, -5355984871255569700913, 333392838283336197688741

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} (-2*n+3*k-1)^(n-k) * binomial(2*n-2*k+1,k)/( (2*n-2*k+1)*(n-k)! ).

Prog

(PARI) a(n) = n!*sum(k=0, n, (-2*n+3*k-1)^(n-k)*binomial(2*n-2*k+1, k)/((2*n-2*k+1)*(n-k)!));

Crossrefs

Cf. A379868, A379877, A379909.

Cf. A379858, A379875.

Sequence in context: A339710 A112119 A369024 * A371027 A058575 A380044

Adjacent sequences: A379853 A379854 A379855 * A379858 A379859 A379860

Keyword

sign,new

Author

Seiichi Manyama, Jan 05 2025

Status

approved