OFFSET
1,1
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..19
EXAMPLE
L.g.f. of A293598: Q(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)) +...
Explicitly,
Q(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 +...
This sequence equals the coefficient of x^(2^n+1)/(2^n+1) in Q(x) for n>=1.
MATHEMATICA
nmax = 10; 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 + 2]], {n, 1, nmax}] (* Vaclav Kotesovec, Oct 15 2017 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 12 2017
STATUS
approved