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Search: id:A156303
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| A156303 |
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G.f.: A(x) = exp( Sum_{n>=1} sigma(n^2)*x^n/n ), a power series in x with integer coefficients. |
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2
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| 1, 1, 4, 8, 20, 38, 88, 162, 336, 624, 1211, 2195, 4109, 7295, 13190, 23072, 40618, 69838, 120486, 204006, 345595, 577387, 962961, 1588483, 2613930, 4262138, 6928799, 11179251, 17976330, 28720552, 45729595, 72401921, 114239033
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Compare with g.f. for partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.
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FORMULA
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a(n) = (1/n)*Sum_{k=1..n} sigma(k^2) * a(n-k) for n>0, with a(0)=1.
Euler transform of Dedekind psi function, cf. A001615. [From Vladeta Jovovic (vladeta(AT)eunet.yu), Feb 12 2009]
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 8*x^3 + 20*x^4 + 38*x^5 + 88*x^6 +...
log(A(x)) = x + 7*x^2/2 + 13*x^3/3 + 31*x^4/4 + 31*x^5/5 + 127*x^6/6 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m^2)*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sigma(k^2)*a(n-k)))}
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CROSSREFS
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Cf. A000203 (sigma), A000041 (partitions).
Sequence in context: A133628 A097940 A032280 this_sequence A008136 A047196 A009889
Adjacent sequences: A156300 A156301 A156302 this_sequence A156304 A156305 A156306
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 08 2009
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