A301409
G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x^2*A(x)/(1 - 2*x*A(x) - 2*x^2*A(x)/(1 - 3*x*A(x) - 3*x^2*A(x)/(1 - ...)))), a continued fraction.
Original entry on oeis.org
1, 1, 3, 11, 47, 221, 1115, 5947, 33231, 193453, 1169239, 7322827, 47479855, 318661109, 2214609419, 15948123771, 119101155215, 923085573061, 7428862280327, 62094175343547, 538956428549743, 4854974080968669, 45347892277523467, 438688081755797051, 4389356528040108847
Offset: 0
G.f. A(x) = 1 + x + 3*x^2 + 11*x^3 + 47*x^4 + 221*x^5 + 1115*x^6 + 5947*x^7 + 33231*x^8 + ...
A301412
G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x*A(x)/(1 - x^2*A(x)/(1 - x^2*A(x)/(1 - x^3*A(x)/(1 - x^3*A(x)/(1 - ...))))))), a continued fraction.
Original entry on oeis.org
1, 1, 3, 11, 46, 205, 957, 4614, 22803, 114898, 588052, 3048612, 15975922, 84489890, 450363757, 2417104782, 13050778500, 70841037919, 386357165119, 2116097719571, 11634392901981, 64188480019008, 355255552604237, 1971866447509917, 10973973061151433, 61222237473973758
Offset: 0
G.f. A(x) = 1 + x + 3*x^2 + 11*x^3 + 46*x^4 + 205*x^5 + 957*x^6 + 4614*x^7 + 22803*x^8 + 114898*x^9 + ...
A301833
G.f. A(x) satisfies: A(x) = 1/(1 - 2*x*A(x)/(1 - 2*x*A(x)/(1 - 4*x*A(x)/(1 - 4*x*A(x)/(1 - 6*x*A(x)/(1 - 6*x*A(x)/(1 - ...))))))), a continued fraction.
Original entry on oeis.org
1, 2, 12, 104, 1104, 13472, 183488, 2749056, 44996864, 802443776, 15579089920, 329170937856, 7562372632576, 188526816632832, 5083702487990272, 147676990509580288, 4600624321049722880, 153012055369679241216, 5409813656756850262016, 202534832564335070937088, 8001606648308588124045312
Offset: 0
G.f. A(x) = 1 + 2*x + 12*x^2 + 104*x^3 + 1104*x^4 + 13472*x^5 + 183488*x^6 + 2749056*x^7 + 44996864*x^8 + ...
log(A(x)) = 2*x + 20*x^2/2 + 248*x^3/3 + 3472*x^4/4 + 53152*x^5/5 + 878144*x^6/6 + ... + A293471(n)*x^n/n + ...
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Table[SeriesCoefficient[(1 + Sum[(2*k)!!*x^k, {k, 1, n}])^(n+1)/(n+1), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 05 2021 *)