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

0,3

Comments

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

Links

Table of n, a(n) for n=0..19.

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

Cf. A000254.

Sequence in context: A318121 A357785 A369229 * A102129 A164310 A369486

Adjacent sequences: A097419 A097420 A097421 * A097423 A097424 A097425

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