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A307762 L.g.f.: log(Product_{k>=1} (1 + x^k/(1 + x))) = Sum_{k>=1} a(k)*x^k/k. 1

%I

%S 1,-1,7,-13,36,-67,141,-269,547,-1076,2146,-4231,8399,-16661,33177,

%T -66109,131921,-263353,526054,-1051108,2100840,-4199614,8396289,

%U -16788239,33570311,-67131715,134250784,-268483361,536940598,-1073843297,2147631641,-4295183165,8590249609,-17180328793

%N L.g.f.: log(Product_{k>=1} (1 + x^k/(1 + x))) = Sum_{k>=1} a(k)*x^k/k.

%F Product {k>=1} (1 + x^k/(1 + x)) = exp(Sum_{k>=1} a(k)*x^k/k).

%e 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 + ... .

%e 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 + ... .

%o (PARI) N=66; x='x+O('x^N); Vec(x*deriv(log(prod(k=1, N, 1+x^k/(1+x)))))

%o (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)))))

%Y Cf. A307602, A307674, A307675, A307761.

%K sign

%O 1,3

%A _Seiichi Manyama_, Apr 27 2019

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Last modified August 5 10:01 EDT 2021. Contains 346464 sequences. (Running on oeis4.)