|
%I #20 Jun 26 2021 08:58:01
%S 1,1,4,21,147,1250,12633,147497,1947676,28699373,466994003,8309274754,
%T 160368858609,3336869582657,74468098634660,1773827462044421,
%U 44905503103938915,1203843692164105458,34070243272290551113,1015056385225183643721
%N E.g.f.: Product_{k>=1} 1/(1 - (exp(x) - 1)^k)^(1/k).
%C Stirling transform of A028342.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F E.g.f.: exp( Sum_{k>=1} d(k) * (exp(x) - 1)^k / k ), where d(n) is the number of divisors of n.
%F a(n) = Sum_{k=0..n} Stirling2(n,k) * A028342(k).
%t max = 19; Range[0, max]! * CoefficientList[Series[Product[1/(1 - (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* _Amiram Eldar_, Jun 26 2021 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(exp(x)-1)^k)^(1/k))))
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N,numdiv(k)*(exp(x)-1)^k/k))))
%Y Cf. A000005, A028342, A048993, A167137, A294363, A305986, A345750, A345751.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 26 2021
|
