A307762 L.g.f.: log(Product_{k>=1} (1 + x^k/(1 + x))) = Sum_{k>=1} a(k)*x^k/k.
1, -1, 7, -13, 36, -67, 141, -269, 547, -1076, 2146, -4231, 8399, -16661, 33177, -66109, 131921, -263353, 526054, -1051108, 2100840, -4199614, 8396289, -16788239, 33570311, -67131715, 134250784, -268483361, 536940598, -1073843297, 2147631641, -4295183165, 8590249609, -17180328793
Offset: 1
Keywords
Examples
L.g.f.: L(x) = x/1 - x^2/2 + 7*x^3/3 - 13*x^4/4 + 36*x^5/5 - 67*x^6/6 + 141*x^7/7 - 269*x^8/8 + ... . exp(L(x)) = 1 + x + 2*x^3 - x^4 + 4*x^5 - 2*x^6 + 5*x^7 - x^8 + ... + A307602(n)*x^n + ... .
Programs
-
PARI
N=66; x='x+O('x^N); Vec(x*deriv(log(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)/(d*(1+x)^d)))))
Formula
Product {k>=1} (1 + x^k/(1 + x)) = exp(Sum_{k>=1} a(k)*x^k/k).