A087751 Weighted sum of the harmonic numbers.

0, 1, 7, 56, 538, 6124, 81048, 1226112, 20902992, 396857376, 8308373760, 190212376320, 4728556327680, 126865966625280, 3654264347274240, 112484501485977600, 3685202487258163200, 128039255560187596800

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = 2*n*a(n-1) + (n-1)!*(2^n-1); a(0)=0, a(1)=1. a(n)=n! * sum(j=1, n, binomial(n, j)*H(j)), where H(j)=sum(k=1, j, 1/k).

E.g.f.: log((2*x-1)/(x-1))/(2*x-1). a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*2^(n-k)*binomial(n, k)/k. a(n) = n!*Sum_{k=1..n} 2^(n-k)*(2^k-1)/k. - Vladeta Jovovic, Aug 12 2005

a(n) ~ n! * log(n) * 2^n * (1 + (gamma-log(2))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jun 03 2022

Prog

(PARI) H(n)=sum(j=1, n, 1/j); a(n)=n!*sum(j=1, n, binomial(n, j)*H(j))

Crossrefs

Cf. A103213, A068102.

Sequence in context: A144263 A001730 A259900 * A099345 A245249 A110830

Adjacent sequences: A087748 A087749 A087750 * A087752 A087753 A087754

Keyword

easy,nonn

Author

Nicholas C. Singer (nsinger2(AT)cox.net), Oct 02 2003

Status

approved