OFFSET
0,3
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
KEYWORD
easy,nonn
AUTHOR
Nicholas C. Singer (nsinger2(AT)cox.net), Oct 02 2003
STATUS
approved