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A097422 Sum{k=1 to n} H(k) k!, where H(k) = sum{j=1 to k} 1/j. 3


%S 0,1,4,15,65,339,2103,15171,124755,1151331,11779971,132323811,

%T 1618766691,21421525731,304887173091,4644050174691,75378332568291,

%U 1298783923147491,23675771981669091,455240918799307491

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

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

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

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

%o (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)

%Y Cf. A000254.

%K easy,nonn

%O 0,3

%A _Leroy Quet_, Aug 21 2004

%E More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and _Robert G. Wilson v_, Aug 23 2004

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)