A180218 a(n) = (n+2)! * Sum_{k=1..n} 1/k.

0, 6, 36, 220, 1500, 11508, 98784, 940896, 9862560, 112923360, 1402980480, 18804839040, 270532604160, 4158579398400, 68031755366400, 1180252336435200, 21644690412441600, 418404711978086400, 8503255462238208000, 181257361663408128000, 4043861992983859200000, 94239874254766141440000

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = (n+1) * (n+2) * A000254(n). - Joerg Arndt, Aug 13 2014

E.g.f.: (x^2-4*x+2*log(1-x))/(x-1)^3.

a(n) = (n+2)/n *((2*n-1)*a(n-1) - (n^2-1)*a(n-2)). - Robert Israel, Aug 13 2014

a(n) ~ exp(-n)*n^(n+5/2)*sqrt(2*Pi)*log(n). - Stefano Spezia, Sep 07 2025

Maple

h:=n-> sum(1/k, k=1..n):seq((n+2)!*h(n), n=0..20);

Crossrefs

Cf. A000254.

Sequence in context: A082309 A004319 A129324 * A218991 A351056 A166748

Adjacent sequences: A180215 A180216 A180217 * A180219 A180220 A180221

Keyword

nonn

Author

Gary Detlefs, Aug 15 2010

Extensions

a(19)-a(21) from Stefano Spezia, Sep 07 2025

Status

approved