A380042 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)^2) ).
1, 1, 5, 48, 697, 13640, 336771, 10053778, 352334753, 14183529480, 645073504435, 32715111226886, 1830671281889649, 112049330303532388, 7446824171300128811, 534068807341887943770, 41111698162393482004801, 3381089519620006418116976, 295869084136630532211207843
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(serreverse(x/(1+2*x*exp(x)))/x))) -
PARI
a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n+1/2, k)/(n-k)!)/(2*n+1);
Formula
E.g.f.: sqrt( (1/x) * Series_Reversion(x/(1 + 2*x*exp(x))) ).
a(n) = (n!/(2*n+1)) * Sum_{k=0..n} 2^k * k^(n-k) * binomial(n+1/2,k)/(n-k)!.