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A097422
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Sum{k=1 to n} H(k) k!, where H(k) = sum{j=1 to k} 1/j.
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3
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0, 1, 4, 15, 65, 339, 2103, 15171, 124755, 1151331, 11779971, 132323811, 1618766691, 21421525731, 304887173091, 4644050174691, 75378332568291, 1298783923147491, 23675771981669091, 455240918799307491
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OFFSET
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0,3
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COMMENTS
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H(k) k! = s(k+1,2), where s() is an unsigned Stirling number of the first kind (A000254).
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LINKS
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Table of n, a(n) for n=0..19.
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EXAMPLE
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a(3) = 1*1 + (1 +1/2)*2 + (1 +1/2 +1/3)*6 = 15
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MATHEMATICA
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a[n_] := Sum[ HarmonicNumber[k]k!, {k, 1, n}]; Table[ a[n], {n, 0, 20}] (* Robert G. Wilson v, Aug 26 2004 *)
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PROG
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(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)
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CROSSREFS
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Cf. A000254.
Sequence in context: A349202 A318121 A357785 * A102129 A164310 A011967
Adjacent sequences: A097419 A097420 A097421 * A097423 A097424 A097425
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet, Aug 21 2004
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EXTENSIONS
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More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and Robert G. Wilson v, Aug 23 2004
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STATUS
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approved
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