OFFSET
0,3
COMMENTS
H(k) k! = s(k+1,2), where s() is an unsigned Stirling number of the first kind (A000254).
EXAMPLE
a(3) = 1*1 + (1 +1/2)*2 + (1 +1/2 +1/3)*6 = 15
MATHEMATICA
a[n_] := Sum[ HarmonicNumber[k]k!, {k, 1, n}]; Table[ a[n], {n, 0, 20}] (* Robert G. Wilson v, Aug 26 2004 *)
PROG
(PARI) hh(n)=sum(i=1, n, 1/i); ff(n)=sum(k=1, n, hh(k)*k!); for (i=1, 30, print1(ff(i), ", ")) (Bouayoun)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Aug 21 2004
EXTENSIONS
More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and Robert G. Wilson v, Aug 23 2004
STATUS
approved