A307675 L.g.f.: log(Product_{k>=1} 1/(1 - x^k/(1 + x))) = Sum_{k>=1} a(k)*x^k/k.
1, 1, 1, 5, -4, 19, -27, 61, -89, 156, -230, 383, -597, 981, -1549, 2493, -3943, 6301, -10012, 16020, -25626, 41174, -66193, 106639, -171829, 277083, -446858, 721033, -1163798, 1879329, -3035767, 4905405, -7928249, 12816369, -20721187, 33505745
Offset: 1
Keywords
Examples
L.g.f.: L(x) = x/1 + x^2/2 + x^3/3 + 5*x^4/4 - 4*x^5/5 + 19*x^6/6 - 27*x^7/7 + 61*x^8/8 - ... . exp(L(x)) = 1 + x + x^2 + x^3 + 2*x^4 + x^5 + 4*x^6 + 8*x^8 + ... + A307626(n)*x^n + ... .
Programs
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PARI
N=66; x='x+O('x^N); Vec(x*deriv(log(1/prod(k=1, N, 1-x^k/(1+x))))) -
PARI
N=66; x='x+O('x^N); Vec(x*deriv(sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1+x)^d)))))
Formula
Product {k>=1} 1/(1 - x^k/(1 + x)) = exp(Sum_{k>=1} a(k)*x^k/k).