A356401 a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!).
1, 2, 9, 25, 150, 841, 6608, 41945, 437986, 4364741, 51640952, 526219585, 7319856206, 102469338245, 1671439939276, 23909485105217, 427384036676690, 7518024186420421, 149244833247716000, 2756811766466473601, 61545779138627817622, 1354007126970517958885
Offset: 1
Keywords
Programs
-
PARI
a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!)));
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)/(1-x))) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)/(1-x)))
Formula
E.g.f.: -(1/(1-x)) * Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k.
E.g.f.: (1/(1-x)) * Sum_{k>0} log(1+x^k)/k!.