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A293598
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L.g.f.: Sum_{n>=1} x^((2*n-1)^2) / ( (2*n-1) * (1 - x^(2*n))^(2*n-1) ).
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4
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1, 3, 5, 7, 12, 11, 26, 15, 51, 19, 91, 23, 155, 27, 232, 62, 341, 35, 592, 39, 656, 344, 870, 47, 1820, 51, 1431, 1441, 1843, 59, 4758, 63, 2925, 4489, 3197, 71, 11899, 75, 4466, 11376, 7650, 83, 23052, 87, 12816, 25025, 7936, 95, 57133, 99, 10706, 49131, 37220, 107, 79570, 2146, 62828, 89263, 15951, 119, 228096, 123, 19500, 152146, 169033, 18864, 218253, 135, 267972, 246308, 75153, 143, 724159, 147, 33227, 490146, 629034, 155, 512448, 159
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OFFSET
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1,2
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LINKS
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EXAMPLE
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L.g.f.: A(x) = x + 3*x^3/3 + 5*x^5/5 + 7*x^7/7 + 12*x^9/9 + 11*x^11/11 + 26*x^13/13 + 15*x^15/15 + 51*x^17/17 + 19*x^19/19 + 91*x^21/21 + 23*x^23/23 + 155*x^25/25 + 27*x^27/27 + 232*x^29/29 + 62*x^31/31 + 341*x^33/33 + 35*x^35/35 + 592*x^37/37 + 39*x^39/39 + 656*x^41/41 + 344*x^43/43 + 870*x^45/45 + 47*x^47/47 + 1820*x^49/49 + 51*x^51/51 + 1431*x^53/53 + 1441*x^55/55 + 1843*x^57/57 + 59*x^59/59 + 4758*x^61/61 + 63*x^63/63 + 2925*x^65/65 +...
which may be written as
A(x) = x/(1 - x^2) + x^9/(3*(1 - x^4)^3) + x^25/(5*(1 - x^6)^5) + x^49/(7*(1 - x^8)^7) + x^81/(9*(1 - x^10)^9) + x^121/(11*(1 - x^12)^11) + x^169/(13*(1 - x^14)^13) +...+ x^((2*n-1)^2) / ((2*n-1)*(1 - x^(2*n))^(2*n-1)) +...
The coefficient of x^(2^n+1)/(2^n+1) in A(x) for n>=1 begins:
[3, 5, 12, 51, 341, 2925, 169033, 33445209, 21619038033, ..., A293599(n), ...].
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MATHEMATICA
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nmax = 80; Table[(CoefficientList[Series[Sum[x^((2*k - 1)^2)/((2*k - 1)*(1 - x^(2*k))^(2*k - 1)), {k, 1, 2*nmax + 1}], {x, 0, 2*nmax + 1}], x] * Range[0, 2*nmax + 1])[[2*n]], {n, 1, nmax}] (* Vaclav Kotesovec, Oct 15 2017 *)
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PROG
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(PARI) {a(n) = my(A, Ox = O(x^(2*n+1)));
A = sum(m=1, sqrtint(n+1), x^((2*m-1)^2) / ( (2*m-1) * (1 - x^(2*m) +Ox)^(2*m-1) ) );
(2*n-1)*polcoeff(A, 2*n-1)}
for(n=1, 80, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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