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 A295239 Expansion of e.g.f. 2/(1 + sqrt(1 + 4*x*exp(x))). 1
 1, -1, 2, -9, 68, -705, 9234, -146209, 2717000, -57986433, 1397949830, -37576332321, 1114326129564, -36141571087297, 1272713716466906, -48360394499269665, 1972269941821097744, -85929979225787811585, 3983422470176606823054, -195765982110500512129057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA E.g.f.: 1/(1 + x*exp(x)/(1 + x*exp(x)/(1 + x*exp(x)/(1 + x*exp(x)/(1 + ...))))), a continued fraction. a(n) ~ sqrt(2*(1+LambertW(-1/4))) * n^(n-1) / (exp(n) * (LambertW(-1/4))^n). - Vaclav Kotesovec, Nov 18 2017 MAPLE a:=series(2/(1+sqrt(1+4*x*exp(x))), x=0, 20): seq(n!*coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 27 2019 MATHEMATICA nmax = 19; CoefficientList[Series[2/(1 + Sqrt[1 + 4 x Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]! nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[x Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[(-1)^(n - k) Binomial[n, k] k! Sum[(-1)^m (m + 1)^(k - m - 1) Binomial[2 m, m]/(k - m)!, {m, 0, k}], {k, 0, n}], {n, 0, 19}] CROSSREFS Cf. A000108, A006531, A052895, A295238. Sequence in context: A336588 A322612 A186183 * A120020 A200248 A180747 Adjacent sequences:  A295236 A295237 A295238 * A295240 A295241 A295242 KEYWORD sign AUTHOR Ilya Gutkovskiy, Nov 18 2017 STATUS approved

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Last modified January 24 13:48 EST 2022. Contains 350538 sequences. (Running on oeis4.)