A307674 L.g.f.: log(Product_{k>=1} 1/(1 - x^k/(1 - x))) = Sum_{k>=1} a(k)*x^k/k.

1, 5, 13, 29, 56, 107, 197, 365, 679, 1280, 2432, 4679, 9075, 17729, 34823, 68701, 135967, 269765, 536200, 1067284, 2126648, 4240978, 8462667, 16895039, 33742281, 67408931, 134697820, 269204657, 538104774, 1075723097, 2150667905, 4300088957, 8598178019

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Formula

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

Example

L.g.f.: L(x) = x/1 + 5*x^2/2 + 13*x^3/3 + 29*x^4/4 + 56*x^5/5 + 107*x^6/6 + 197*x^7/7 + 365*x^8/8 + ... .
exp(L(x)) = 1 + x + 3*x^2 + 7*x^3 + 16*x^4 + 35*x^5 + 76*x^6 + 162*x^7 + 342*x^8 + ... + A227682(n)*x^n + ... .

Prog

(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)))))

Crossrefs

Cf. A227682, A307599, A307675.

Sequence in context: A086732 A162329 A299895 * A273026 A273077 A160430

Adjacent sequences: A307671 A307672 A307673 * A307675 A307676 A307677

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2019

Status

approved