A185301 G.f.: exp( Sum_{n>=1} Sum_{k>=1} sigma(n)^k * x^(n*k) / n ).

1, 1, 3, 5, 14, 20, 59, 83, 229, 350, 878, 1302, 3479, 5068, 12640, 19357, 47547, 71173, 175029, 262445, 635297, 966680, 2288213, 3470143, 8266788, 12507003, 29283071, 44756825, 104067224, 158535387, 367088494, 559952784, 1287857188, 1971948577

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Formula

Logarithmic derivative yields A185302.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 14*x^4 + 20*x^5 + 59*x^6 + 83*x^7 +...
such that, by definition:
log(A(x)) = (x + x^2 + x^3 + x^4 +...+ x^k +...)/1
 + (3*x^2 + 9*x^4 + 27*x^6 + 81*x^8 +...+ 3^k*x^(2*k) +...)/2
 + (4*x^3 + 16*x^6 + 64*x^9 + 256*x^12 +...+ 4^k*x^(3*k) +...)/3
 + (7*x^4 + 49*x^8 + 343*x^12 + 2401*x^16 +...+ 7^k*x^(4*k) +...)/4 +...
= x + 5*x^2/2 + 7*x^3/3 + 29*x^4/4 + 11*x^5/5 + 131*x^6/6 +...+ A185302(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=1, n\m, sigma(m)^k*x^(m*k)/m), x*O(x^n))), n)}

Crossrefs

Cf. A185302.

Sequence in context: A331996 A179213 A074378 * A179304 A026645 A026667

Adjacent sequences: A185298 A185299 A185300 * A185302 A185303 A185304

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2012

Status

approved