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 A320651 Expansion of 1/(1 - Sum_{k>=1} k*x^k/(1 + x^k)). 1
 1, 1, 2, 7, 14, 36, 90, 213, 520, 1271, 3082, 7493, 18238, 44324, 107782, 262142, 637368, 1549870, 3768886, 9164499, 22285034, 54190024, 131771616, 320424614, 779166270, 1894671121, 4607207304, 11203190618, 27242414612, 66244451632, 161084380040, 391703392954 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Invert transform of A000593. LINKS N. J. A. Sloane, Transforms FORMULA G.f.: 1/(1 - x * (d/dx) log(Product_{k>=1} (1 + x^k))). G.f.: 24/(25 - theta_2(x)^4 - theta_3(x)^4), where theta_() is the Jacobi theta function. a(0) = 1; a(n) = Sum_{k=1..n} A000593(k)*a(n-k). MAPLE a:=series(1/(1-add(k*x^k/(1+x^k), k=1..100)), x=0, 32): seq(coeff(a, x, n), n=0..31); # Paolo P. Lava, Apr 02 2019 MATHEMATICA nmax = 31; CoefficientList[Series[1/(1 - Sum[k x^k/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x] nmax = 31; CoefficientList[Series[24/(25 - EllipticTheta[2, 0, x]^4 - EllipticTheta[3, 0, x]^4), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[Sum[Mod[d, 2] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 31}] CROSSREFS Cf. A000009, A000593, A180305, A320650. Sequence in context: A191396 A173126 A256272 * A167762 A191389 A191319 Adjacent sequences:  A320648 A320649 A320650 * A320652 A320653 A320654 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 18 2018 STATUS approved

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Last modified February 26 01:28 EST 2020. Contains 332270 sequences. (Running on oeis4.)