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A355719
Expansion of e.g.f. exp( x/(1 - log(1+x)) ).
2
1, 1, 3, 10, 45, 231, 1405, 9472, 72177, 596845, 5442631, 53052726, 561826309, 6286949787, 75704999721, 954108249676, 12862823623393, 179921659771257, 2683989118991467, 41178997678745506, 673670267643931581, 11223738258484213519, 200027545794685345749
OFFSET
0,3
COMMENTS
a(43) is negative. - Vaclav Kotesovec, Jul 15 2022
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A108125(k) * binomial(n-1,k-1) * a(n-k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-log(1+x)))))
(PARI) a006252(n) = sum(k=0, n, k!*stirling(n, k, 1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*a006252(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 15 2022
STATUS
approved