OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..439
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n, k)|*A000248(k).
From Paul D. Hanna, Mar 17 2010: (Start)
E.g.f.: exp( Sum_{n>=1} H(n)*x^n ) where H(n) is the n-th harmonic number;
a(n) = (n-1)!*Sum_{k=0..n-1} (n-k)*H(n-k)*a(k)/k! for n>0 with a(0)=1. (End)
Empirical: a(n) = Sum_{i=0..n} binomial(n,i)*A005727(i)*(n-1)!/(i-1)! for n>0. - John M. Campbell, Dec 13 2016
MATHEMATICA
Table[Sum[BellY[n, k, Table[m! HarmonicNumber[m], {m, n}]], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *)
PROG
(PARI) a(n)=if(n==0, 1, (n-1)!*sum(k=0, n-1, (n-k)*sum(j=1, n-k, 1/j)*a(k)/k!)) \\ Paul D. Hanna, Mar 17 2010; corrected Mar 19 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 02 2003
STATUS
approved