A307761 L.g.f.: log(Product_{k>=1} (1 + x^k/(1 - x))) = Sum_{k>=1} a(k)*x^k/k.

1, 3, 7, 11, 16, 21, 29, 35, 43, 48, 56, 65, 79, 87, 97, 99, 103, 111, 134, 156, 182, 190, 185, 161, 141, 133, 178, 263, 378, 471, 497, 387, 161, -133, -341, -313, 75, 782, 1645, 2300, 2379, 1596, -42, -2222, -4232, -5241, -4464, -1551, 3263, 9023, 14287, 17249, 16219, 9912, -2074

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

L.g.f.: L(x) = x/1 + 3*x^2/2 + 7*x^3/3 + 11*x^4/4 + 16*x^5/5 + 21*x^6/6 + 29*x^7/7 + 35*x^8/8 + ... .
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 7*x^4 + 12*x^5 + 20*x^6 + 33*x^7 + 53*x^8 + ... + A126348(n)*x^n + ... .

Prog

(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)))))

Crossrefs

Cf. A126348, A307674, A307675, A307762.

Sequence in context: A117829 A166092 A184913 * A022821 A001618 A118027

Adjacent sequences: A307758 A307759 A307760 * A307762 A307763 A307764

Keyword

sign

Author

Seiichi Manyama, Apr 27 2019

Status

approved