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A226890

E.g.f.: exp( Sum_{n>=1} sigma(n,n) * x^(n^2) / n^n ).

1, 1, 1, 1, 31, 151, 451, 1051, 33601, 663601, 5187001, 25905001, 254322751, 10408719751, 128046088171, 920598820051, 29249420054401, 723848667813601, 12441294278905201, 138598703861148241, 4406639731521827551, 93453608310743628151, 1932981245635597160851, 27744052310106087405451

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OFFSET

0,5

COMMENTS

Here sigma(n,n) = A023887(n), the sum of the n-th powers of the divisors of n.

Compare to: exp( Sum_{n>=1} sigma(n)*x^n/n ), the g.f. of the partitions.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) == 1 (mod 30) (conjecture - valid up to n=4000; if true for n>=0, why?).

EXAMPLE

E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 31*x^4/4! + 151*x^5/5! + 451*x^6/6! +...