A203557 G.f.: exp( Sum_{n>=1} sigma(n^5)*x^n/n ).

1, 1, 32, 153, 1145, 5677, 37641, 184685, 1047862, 5196410, 26935148, 129702476, 638028933, 2987297287, 14055935617, 64139004752, 291595380989, 1296984485909, 5732084828019, 24910785830408, 107411267744602, 457008372687439, 1928413165110846, 8046605441623654

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

Logarithmic derivative yields A203556.

a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A203556(k)*a(n-k) for n > 0. - Seiichi Manyama, Sep 09 2020

Example

G.f.: A(x) = 1 + x + 32*x^2 + 153*x^3 + 1145*x^4 + 5677*x^5 + 37641*x^6 +...
where the logarithm equals the l.g.f. of A203556:
log(A(x)) = x + 63/2*x^2 + 364/3*x^3 + 2047/4*x^4 + 3906/5*x^5 +...+ sigma(n^5)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m^5)*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A203556, A000203 (sigma); variants: A000041, A156303, A156304, A202993.

Sequence in context: A220975 A100172 A234132 * A124998 A126419 A197621

Adjacent sequences: A203554 A203555 A203556 * A203558 A203559 A203560

Keyword

nonn

Author

Paul D. Hanna, Jan 03 2012

Status

approved