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E.g.f.: 1/(1-x)/sqrt(1-2*x). - Vladeta Jovovic, May 11 2003
a(n) = Integral_{x=-infinity..infinity} x^(2*n+1)*exp(-x^2)*erfi(x/sqrt(2)), with erfi the imaginary error function. - Groux Roland, Mar 26 2011
E.g.f.: d/dx(F(x)^(-1)) where (-1) denotes the compositional inverse and F(x) = sin(x)/(1+sin(x)) = x - 2*x^2/2! + 5*x^3/3! - 16*x^4/4! + .... See A000111. - Peter Bala, Jun 24 2012
E.g.f.: E(x) = 1/sqrt(1-2*x)/(1-x) = (1 + x/(U(0)-x))/(1-x), where U(k) = (2*k+1)*x + (k+1) - (k+1)*(2*k+3)*x/U(k+1); (continued fraction Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Jun 27 2012
G.f.: hypergeom([1,1/2],[],2*x)^2. - Mark van Hoeij, May 16 2013
a(n-1)*n = A233481(n) for n >= 1. - Peter Luschny, Dec 14 2013
a(n) = (3*n-1)*a(n-1)-(2*n-1)*(n-1)*a(n-2) for n >= 2. - Peter Luschny, Dec 14 2013
a(n) ~ 2^(n+3/2) * n^n / exp(n). - Vaclav Kotesovec, Dec 20 2013
a(n) = 2*Pochhammer(1/2, n+1)*hyper2F1([1/2, -n], [3/2], -1). - Peter Luschny, Aug 02 2014
a(n) = -(2*n+1)!! * 2^(-n-1) * Im(Beta(2, n+1, 1/2)). - Vladimir Reshetnikov, Apr 23 2016
Expansion of square of continued fraction 1/(1 - x/(1 - 2*x/(1 - 3*x/(1 - 4*x/(1 - 5*x/(1 - ...)))))). - Ilya Gutkovskiy, Apr 19 2017
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