|
%I #19 Sep 07 2018 05:04:23
%S 1,1,3,31,145,1641,17731,194503,2676801,40644145,667689571,
%T 11514903951,227665389073,4578990563161,100913115588195,
%U 2372334731747191,57930324367791361,1509398686720812513,41341036374519788611,1184009909077133031295
%N E.g.f.: exp(Sum_{n>=1} A000593(n) * x^n).
%H Seiichi Manyama, <a href="/A294394/b294394.txt">Table of n, a(n) for n = 0..434</a>
%F a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A000593(k)*a(n-k)/(n-k)! for n > 0.
%F a(n) ~ Pi^(1/3) * exp((3*Pi)^(2/3) * n^(2/3) / 2^(4/3) - 1/24 - n) * n^(n - 1/6) / (2^(1/6) * 3^(2/3)). - _Vaclav Kotesovec_, Sep 07 2018
%t a[n_] := a[n] = If[n == 0, 1, Sum[k*Sum[-(-1)^d*k/d, {d, Divisors[k]}]*a[n - k], {k, 1, n}]/n]; Table[n!*a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Sep 07 2018 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, d*(d%2))*x^k))))
%Y E.g.f.: exp(Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294392 (k=0), this sequence (k=1), A294395 (k=2).
%Y Cf. A000009, A000593, A301799, A301800.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 30 2017
|
