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 A097422 Sum{k=1 to n} H(k) k!, where H(k) = sum{j=1 to k} 1/j. 3
 0, 1, 4, 15, 65, 339, 2103, 15171, 124755, 1151331, 11779971, 132323811, 1618766691, 21421525731, 304887173091, 4644050174691, 75378332568291, 1298783923147491, 23675771981669091, 455240918799307491 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS H(k) k! = s(k+1,2), where s() is an unsigned Stirling number of the first kind (A000254). LINKS 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: A349202 A318121 A357785 * A102129 A164310 A011967 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

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)