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A293597 L.g.f.: Sum_{n>=1} (x - x^(2*n-1))^(2*n-1) / (2*n-1).

%I A293597 #5 Oct 12 2017 23:29:53
%S A293597 0,1,-4,8,-11,1,14,1,-50,58,1,1,-54,1,-28,311,-340,1,75,1,-81,345,-44,
%T A293597 1,-1427,1531,-52,496,-1253,1,1343,1,-2924,738,-68,9444,-10073,1,-76,
%U A293597 1028,3691,1,-4691,1,-6941,21295,-92,1,-55580,33034,28180,1752,-11479,1,-54063,42847,19437,2186,-116,1,-77934,1,-124,238507,-169032,85151,-188859,1,-25755,3198,432636,1,-513328,1,-148,157041,-36005,711327,-465347,1
%N A293597 L.g.f.: Sum_{n>=1} (x - x^(2*n-1))^(2*n-1) / (2*n-1).
%H A293597 Paul D. Hanna, <a href="/A293597/b293597.txt">Table of n, a(n) for n = 1..2050</a>
%e A293597 L.g.f.: A(x) = x^3/3 - 4*x^5/5 + 8*x^7/7 - 11*x^9/9 + x^11/11 + 14*x^13/13 + x^15/15 - 50*x^17/17 + 58*x^19/19 + x^21/21 + x^23/23 - 54*x^25/25 + x^27/27 - 28*x^29/29 + 311*x^31/31 - 340*x^33/33 + x^35/35 + 75*x^37/37 + x^39/39 - 81*x^41/41 + 345*x^43/43 - 44*x^45/45 + x^47/47 - 1427*x^49/49 + 1531*x^51/51 - 52*x^53/53 + 496*x^55/55 - 1253*x^57/57 + x^59/59 + 1343*x^61/61 + x^63/63 - 2924*x^65/65 +...
%e A293597 which may be written as
%e A293597 A(x) = (x - x) + (x - x^3)^3/3 + (x - x^5)^5/5 + (x - x^7)^7/7 + (x - x^9)^9/9 + (x - x^11)^11/11 + (x - x^13)^13/13 + (x - x^15)^15/15 + (x - x^17)^17/17 + (x - x^19)^19/19 + (x - x^21)^21/21 +...+ (x - x^(2*n-1))^(2*n-1)/(2*n-1) +...
%e A293597 The coefficient of x^(2^n+1)/(2^n+1) in A(x) for n>=1 begins:
%e A293597 [1, -4, -11, -50, -340, -2924, -169032, -33445208, -21619038032, 1 - A293599(n), ...].
%o A293597 (PARI) {a(n) = my(A, Ox = O(x^(2*n+1)));
%o A293597 A = sum(m=1, n+1, (x - x^(2*m-1) +Ox)^(2*m-1) / (2*m-1) );
%o A293597 (2*n-1)*polcoeff(A, 2*n-1)}
%o A293597 for(n=1, 80, print1(a(n), ", "))
%Y A293597 Cf. A293129, A293598, A293599.
%K A293597 sign
%O A293597 1,3
%A A293597 _Paul D. Hanna_, Oct 12 2017