A299021 G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x*Product_{n>=1} (1 + a(n)*x^n)/(1 - a(n)*x^n).

1, 2, 6, 22, 86, 358, 1558, 6966, 31894, 148918, 705062, 3380054, 16381158, 80056550, 394266950, 1955139942, 9749771926, 48873487942, 246160229782, 1244801094742, 6318514387638, 32184084454166, 164425969781062, 842429440124854, 4327629345403078, 22283328480744070

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Formula

G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x*exp(Sum_{k>=1} Sum_{n>=1} (1 + (-1)^(k+1))*a(n)^k*x^(n*k)/k).

Example

G.f.: A(x) = x + 2*x^2 + 6*x^3 + 22*x^4 + 86*x^5 + ... = x * ((1 + x) * (1 + 2*x^2) * (1 + 6*x^3) * (1 + 22*x^4) * (1 + 86*x^5) * ...) / ((1 - x) * (1 - 2*x^2) * (1 - 6*x^3) * (1 - 22*x^4) * (1 - 86*x^5) * ...).

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[(1 + a[k] x^k)/(1 - a[k] x^k), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 26}]
a[n_] := a[n] = SeriesCoefficient[x Exp[Sum[Sum[(1 + (-1)^(k + 1)) a[j]^k x^(j k)/k, {j, 1, n - 1}], {k, 1, n - 1}]], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 26}]

Crossrefs

Cf. A032305, A073075, A093637.

Sequence in context: A150257 A150258 A073075 * A153475 A150259 A165531

Adjacent sequences: A299018 A299019 A299020 * A299022 A299023 A299024

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 18 2018

Status

approved