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A226890
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E.g.f.: exp( Sum_{n>=1} sigma(n,n) * x^(n^2) / n^n ).
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1
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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
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0,5
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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a(n) == 1 (mod 30) (conjecture - valid up to n=4000; if true for n>=0, why?).
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EXAMPLE
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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! +...
where
log(A(x)) = x + 5*x^4/2^2 + 28*x^9/3^3 + 273*x^16/4^4 + 3126*x^25/5^5 + 47450*x^36/6^6 + 823544*x^49/7^7 +...+ A023887(n)*x^(n^2)/n^n +...
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PROG
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(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, sigma(m, m)*(x^m/m)^m)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
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CROSSREFS
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Cf. A226838, A023887.
Sequence in context: A347109 A142792 A201964 * A104049 A176922 A134553
Adjacent sequences: A226887 A226888 A226889 * A226891 A226892 A226893
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jun 20 2013
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STATUS
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approved
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