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 A320652 Expansion of 1/(2 - Product_{k>=1} 1/(1 - k*x^k)). 1
 1, 1, 4, 13, 45, 147, 497, 1643, 5490, 18252, 60812, 202364, 673915, 2243295, 7468973, 24865272, 82783967, 275605513, 917563193, 3054785032, 10170143277, 33858882922, 112724577088, 375287739083, 1249425198725, 4159643200494, 13848474406054, 46104972636634, 153494780854254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Invert transform of A006906. LINKS Table of n, a(n) for n=0..28. N. J. A. Sloane, Transforms FORMULA G.f.: 1/(1 - Sum_{k>=1} k*x^k / Product_{j=1..k} (1 - j*x^j)). a(0) = 1; a(n) = Sum_{k=1..n} A006906(k)*a(n-k). MAPLE a:=series(1/(2-mul(1/(1-k*x^k), k=1..100)), x=0, 29): seq(coeff(a, x, n), n=0..28); # Paolo P. Lava, Apr 02 2019 MATHEMATICA nmax = 28; CoefficientList[Series[1/(2 - Product[1/(1 - k x^k), {k, 1, nmax}]), {x, 0, nmax}], x] nmax = 28; CoefficientList[Series[1/(1 - Sum[k x^k/Product[(1 - j x^j), {j, 1, k}], {k, 1, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[Total[Times@@@IntegerPartitions[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 28}] CROSSREFS Cf. A006906, A055887, A257674, A299162. Sequence in context: A285188 A192255 A035356 * A203573 A214997 A189348 Adjacent sequences: A320649 A320650 A320651 * A320653 A320654 A320655 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 18 2018 STATUS approved

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Last modified June 8 10:34 EDT 2023. Contains 363163 sequences. (Running on oeis4.)