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A061256
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Euler transform of sigma(n), cf. A000203.
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6
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1, 1, 4, 8, 21, 39, 92, 170, 360, 667, 1316, 2393, 4541, 8100, 14824, 26071, 46422, 80314, 139978, 238641, 408201, 686799, 1156062, 1920992, 3189144, 5238848, 8589850, 13963467, 22641585, 36447544, 58507590, 93334008, 148449417
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| According to a message on a blog page by "Allan" (see http://sbseminar.wordpress.com/2010/10/06/a-peculiar-numerical-coincidence/#comments) it appears that a(n) = number of conjugacy classes of commutative ordered pairs in S_N.
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| G.f.: Product_{k=1..infinity} (1 - x^k)^(-sigma(k)). a(n)=1/n*Sum_{k=1..n} a(n-k)*b(k), n>1, a(0)=1, b(k)=Sum_{d|k} d*sigma(d), cf. A001001.
G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*x^n/(1-x^n)^2 /n ). [From Paul D. Hanna, Mar 28 2009]
Also A(x) = exp( Sum_{n>=1} sigma_2(n)*x^n/(1-x^n)/n ). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Mar 28 2009]
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PROG
| (PARI) N=66; x='x+O('x^N); /* that many terms */
gf=1/prod(j=1, N, eta(x^j)^j);
Vec(gf) /* show terms */ /* Joerg Arndt, May 03 2008 */
(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(m=1, n, sigma(m)*x^m/(1-x^m+x*O(x^n))^2/m)), n))} /* Paul D. Hanna, Mar 28 2009 */
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CROSSREFS
| Cf. A000203, A001001, A006171, A001970, A061255, A061257.
Sequence in context: A094878 A079860 A006908 * A180608 A077921 A097076
Adjacent sequences: A061253 A061254 A061255 * A061257 A061258 A061259
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 21 2001
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