A379875 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)) + x.

1, 0, 1, -4, 29, -256, 2797, -36352, 549145, -9468928, 183661721, -3960254464, 94011364405, -2436944723968, 68503370394565, -2075866971897856, 67464214813124273, -2340885649895194624, 86377064031382020913, -3377541983440381935616, 139515670016074334382541

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A377859, A379876.

Sequence in context: A291103 A385698 A125808 * A367752 A254124 A203970

Adjacent sequences: A379872 A379873 A379874 * A379876 A379877 A379878

Keyword

sign

Author

Seiichi Manyama, Jan 05 2025

Status

approved