A097422 Sum{k=1 to n} H(k) k!, where H(k) = sum{j=1 to k} 1/j.

0, 1, 4, 15, 65, 339, 2103, 15171, 124755, 1151331, 11779971, 132323811, 1618766691, 21421525731, 304887173091, 4644050174691, 75378332568291, 1298783923147491, 23675771981669091, 455240918799307491

Offset: 0

Author

Leroy Quet, Aug 21 2004

Keywords

• easy
• nonn

Comments

H(k) k! = s(k+1,2), where s() is an unsigned Stirling number of the first kind (A000254).

Examples

			a(3) = 1*1 + (1 +1/2)*2 + (1 +1/2 +1/3)*6 = 15
		

Crossrefs

Cf. A000254.

Programs

Mathematica

a[n_] := Sum[ HarmonicNumber[k]k!, {k, 1, n}]; Table[ a[n], {n, 0, 20}] (* Robert G. Wilson v, Aug 26 2004 *)

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)

Extensions

More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and Robert G. Wilson v, Aug 23 2004