A091530 a(n) = Sum_{k=1..n} H(k) k! (n-k)!, where H(k) is the k-th harmonic number.

1, 4, 16, 73, 388, 2396, 17024, 137544, 1248816, 12603288, 140018688, 1698063552, 22318009344, 315942698880, 4791898275840, 77510315197440, 1331759355586560, 24220225133061120, 464796175236710400, 9385769913543475200, 198936154022512435200, 4415822707430415052800

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

E.g.f.: (-li[2]((2-x)*x) + 2*li[2](x) - 2*log(1-x)*(x-1)) / (x-2)^2 + (log(1-x) * (4*x^2 + log(1-x)*x - 14*x - log(1-x) + 12)) / (2*(x-2)^2*(x-1)) where li[2](x) is the dilogarithm of x. - Vladimir Kruchinin, Jan 03 2024

a(n) ~ n! * (log(n) + gamma), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 03 2024

Maple

H:= proc(n) H(n):= `if`(n=0, 0, H(n-1)+1/n) end:
a:= n-> add(H(k)*k!*(n-k)!, k=1..n):
seq(a(n), n=1..22);  # Alois P. Heinz, Jan 03 2024

Mathematica

Table[ Sum[ HarmonicNumber[k]k!(n - k)!, {k, 1, n}], {n, 1, 20}] (* Robert G. Wilson v, Jan 14 2004 *)

Prog

(PARI) a(n) = sum(k=1, n, sum(i=1, k, 1/i)*k!*(n-k)!); \\ Michel Marcus, Jan 03 2024

Crossrefs

Cf. A000142, A001008, A002805, A091528.

Sequence in context: A007234 A096244 A030131 * A344248 A301455 A214372

Adjacent sequences: A091527 A091528 A091529 * A091531 A091532 A091533

Keyword

nonn

Author

Leroy Quet, Jan 08 2004

Extensions

Extended by Robert G. Wilson v, Jan 14 2004

Status

approved