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%I #13 Jan 19 2022 10:17:44
%S 1,-1,3,-2,5,-5,8,-7,13,-13,18,-19,26,-29,39,-40,52,-60,72,-81,101,
%T -113,134,-152,181,-206,243,-273,318,-365,418,-473,549,-620,710,-803,
%U 914,-1034,1177,-1322,1498,-1691,1904,-2139,2416,-2704,3036,-3400,3811,-4261
%N Sequence of coefficients arising in study of generating function for A067619.
%H Vaclav Kotesovec, <a href="/A186545/b186545.txt">Table of n, a(n) for n = 1..1000</a>
%H Arnold Knopfmacher and Neville Robbins, <a href="http://www.plouffe.fr/OEIS/citations/robbinspart.pdf">Identities for the total number of parts in partitions of integers</a>, Util. Math. 67 (2005), 9-18. (See last line of text.)
%t nmax = 50; A067619 = CoefficientList[Series[Sum[k*x^(2*k - 1)*Product[1 + x^(2*j - 1), {j, 1, k - 1}], {k, 1, nmax + 1}], {x, 0, nmax + 1}], x]; A000700 = CoefficientList[Series[Product[1 + x^(2 k + 1), {k, 0, nmax + 1}], {x, 0, nmax + 1}], x]; b = ConstantArray[0, nmax + 1]; b[[1]] = 0; Do[b[[n + 1]] = (A067619[[n + 1]] - Sum[A000700[[n - k + 1]]*b[[k + 1]], {k, 0, n - 1}]) / A000700[[1]], {n, 1, nmax}]; Rest[b] (* _Vaclav Kotesovec_, Jun 28 2016 *)
%K sign
%O 1,3
%A _N. J. A. Sloane_, Feb 23 2011
%E More terms from _Vaclav Kotesovec_, Jun 28 2016