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 A092484 Expansion of Product_{m>=1} (1 + m^2*q^m). 12
 1, 1, 4, 13, 25, 77, 161, 393, 726, 2010, 3850, 7874, 16791, 31627, 69695, 139560, 255997, 482277, 986021, 1716430, 3544299, 6507128, 11887340, 21137849, 38636535, 70598032, 123697772, 233003286, 412142276, 711896765, 1252360770 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sum of squares of products of terms in all partitions of n into distinct parts. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(2*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018 Conjecture: log(a(n)) ~ sqrt(2*n) * (log(2*n) - 2). - Vaclav Kotesovec, Dec 27 2020 EXAMPLE The partitions of 6 into distinct parts are 6, 1+5, 2+4, 1+2+3, the corresponding squares of products are 36, 25, 64, 36 and their sum is a(6) = 161. MAPLE b:= proc(n, i) option remember; (m-> `if`(mn, 0, i^2*b(n-i, i-1)))))(i*(i+1)/2) end: a:= n-> b(n\$2): seq(a(n), n=0..40); # Alois P. Heinz, Sep 10 2017 MATHEMATICA Take[ CoefficientList[ Expand[ Product[1 + m^2*q^m, {m, 100}]], q], 31] (* Robert G. Wilson v, Apr 05 2005 *) PROG (PARI) N=66; x='x+O('x^N); Vec(prod(n=1, N, 1+n^2*x^n)) \\ Seiichi Manyama, Sep 10 2017 CROSSREFS Cf. A022629, A077335, A265844, A285737, A292165. Column k=2 of A292189. Sequence in context: A056708 A307271 A333297 * A091823 A024834 A143867 Adjacent sequences: A092481 A092482 A092483 * A092485 A092486 A092487 KEYWORD nonn AUTHOR Jon Perry, Apr 04 2004 EXTENSIONS More terms from Robert G. Wilson v, Apr 05 2004 STATUS approved

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Last modified October 2 16:19 EDT 2023. Contains 365837 sequences. (Running on oeis4.)