A159308 G.f.: A(x) = exp( Sum_{n>=1} (1 + sigma(n)*x)^n * x^n/n ).
1, 1, 2, 5, 14, 40, 154, 631, 2246, 10476, 71232, 383220, 1553841, 8223567, 58756725, 338290401, 1754330940, 11744499990, 103864469131, 1220564280222, 17394859369497, 214311637862464, 1891506713163679, 10894997683415647
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 154*x^6 +... log(A(x)) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+4*x)^3*x^3/3 + (1+7*x)^4*x^4/4 +... log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 116*x^5/5 + 606*x^6/6 +... (A159309)
Crossrefs
Cf. A159309 (log).
Programs
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PARI
{a(n)=polcoeff(exp(sum(m=1,n+1,(1+sigma(m)*x+x*O(x^n))^m*x^m/m)),n)}