login
A091530
a(n) = Sum_{k=1..n} H(k) k! (n-k)!, where H(k) is the k-th harmonic number.
1
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 08 2004
EXTENSIONS
Extended by Robert G. Wilson v, Jan 14 2004
STATUS
approved