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%I #11 Sep 09 2020 10:13:06
%S 1,1,32,153,1145,5677,37641,184685,1047862,5196410,26935148,129702476,
%T 638028933,2987297287,14055935617,64139004752,291595380989,
%U 1296984485909,5732084828019,24910785830408,107411267744602,457008372687439,1928413165110846,8046605441623654
%N G.f.: exp( Sum_{n>=1} sigma(n^5)*x^n/n ).
%H Seiichi Manyama, <a href="/A203557/b203557.txt">Table of n, a(n) for n = 0..1000</a>
%F Logarithmic derivative yields A203556.
%F a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A203556(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Sep 09 2020
%e G.f.: A(x) = 1 + x + 32*x^2 + 153*x^3 + 1145*x^4 + 5677*x^5 + 37641*x^6 +...
%e where the logarithm equals the l.g.f. of A203556:
%e log(A(x)) = x + 63/2*x^2 + 364/3*x^3 + 2047/4*x^4 + 3906/5*x^5 +...+ sigma(n^5)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,sigma(m^5)*x^m/m)+x*O(x^n)),n)}
%Y Cf. A203556, A000203 (sigma); variants: A000041, A156303, A156304, A202993.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 03 2012
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