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A107742
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G.f.: Product(j>=1, Product(i>=1, 1+x^(i*j) ) ).
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1
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1, 1, 2, 4, 6, 10, 17, 25, 38, 59, 86, 125, 184, 260, 369, 524, 726, 1005, 1391, 1894, 2576, 3493, 4687, 6272, 8373, 11090, 14647, 19294, 25265, 32991, 42974, 55705, 72025, 92895, 119349, 152965, 195592, 249280, 316991, 402215, 508932, 642598, 809739, 1017850, 1276959, 1599015, 1997943, 2491874, 3102477, 3855165, 4782408, 5922954
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| Euler transform of A001227.
Weigh transform of A000005.
G.f. satisfies: log(A(x)) = Sum_{n>=1} A109386(n)/n*x^n, where A109386(n) = Sum_{d|n} d*Sum_{m|d} (m mod 2). [Paul D. Hanna, Jun 26 2005]
G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*x^n/(1-x^(2n)) /n ). [Paul D. Hanna, Mar 28 2009]
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PROG
| (PARI) a(n)=polcoeff(prod(k=1, n, prod(j=1, n\k, 1+x^(j*k)+x*O(x^n))), n) /* Paul D. Hanna */
(PARI)
N=66; x='x+O('x^N); /* that many terms */
gf=1/prod(j=0, N, eta(x^(2*j+1)));
gf=prod(j=1, N, (1+x^j)^numdiv(j)); /* same g.f. */
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^(2*m)+x*O(x^n))/m)), n))} /* Paul D. Hanna, Mar 28 2009 */
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CROSSREFS
| Cf. A006171, A109386.
Sequence in context: A204656 A070689 A091611 * A158510 A004695 A014216
Adjacent sequences: A107739 A107740 A107741 * A107743 A107744 A107745
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 11 2005
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EXTENSIONS
| More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jun 26 2005
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