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 A107742 G.f.: prod(j>=1, prod(i>=1, 1+x^(i*j) ) ). 46
 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; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 N. J. A. Sloane, Transforms 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] G.f.: prod(n>=1, Q(x^n) ) where Q(x) is the g.f. of A000009. [Joerg Arndt, Feb 27 2014] a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A109386(k)*a(n-k) for n > 0. - Seiichi Manyama, Jun 04 2017 Conjecture: log(a(n)) ~ Pi*sqrt(n*log(n)/6). - Vaclav Kotesovec, Aug 29 2018 MATHEMATICA nmax = 50; CoefficientList[Series[Product[(1+x^(i*j)), {i, 1, nmax}, {j, 1, nmax/i}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 04 2017 *) nmax = 50; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 23 2018 *) nmax = 50; s = 1 + x; Do[s *= Sum[Binomial[DivisorSigma[0, k], j]*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]]; , {k, 2, nmax}]; Take[CoefficientList[s, x], nmax + 1] (* Vaclav Kotesovec, Aug 28 2018 *) 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); gf=1/prod(j=0, N, eta(x^(2*j+1))); gf=prod(j=1, N, (1+x^j)^numdiv(j)); Vec(gf) /* 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 */ CROSSREFS Cf. A006171, A109386, A219554, A280473, A280486, A288007. Product_{k>=1} (1 + x^k)^sigma_m(k): this sequence (m=0), A192065 (m=1), A288414 (m=2), A288415 (m=3), A301548 (m=4), A301549 (m=5), A301550 (m=6), A301551 (m=7), A301552 (m=8). Sequence in context: A204656 A070689 A091611 * A228779 A158510 A004695 Adjacent sequences:  A107739 A107740 A107741 * A107743 A107744 A107745 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jun 11 2005 EXTENSIONS More terms from Paul D. Hanna, Jun 26 2005 STATUS approved

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Last modified February 24 22:04 EST 2020. Contains 332216 sequences. (Running on oeis4.)