A333044 Exponential self-convolution of A232690.

1, 2, 6, 26, 146, 1014, 8374, 80282, 875874, 10719734, 145422182, 2166117018, 35143677106, 616926078326, 11650276119702, 235510563023642, 5074238094097538, 116081921186069622, 2810093148179120710, 71767508789469271322, 1928439105298059705042

Offset: 0

Author

Vaclav Kotesovec, Mar 06 2020

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 26*x^3/3! + 146*x^4/4! + 1014*x^5/5! + ...
		

Crossrefs

Cf. A232690.

Programs

Mathematica

CoefficientList[Simplify[Assuming[Element[x, Reals], Series[LambertW[-1, (4*x - 3)*E^(-3)]/(4*x - 3), {x, 0, 20}]]], x] * Range[0, 20]!

PARI

{a(n)=my(A = 1+2*x); for(i=1, n, A = exp(2/sqrt(A)*intformal(A^(3/2) + x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Formula

E.g.f. satisfies: A(x) = exp(2/sqrt(A(x)) * Integral A(x)^(3/2) dx).

E.g.f. LambertW(-1, (4*x-3)*exp(-3))/(4*x-3).

a(n) = Sum_{k=0..n} binomial(n,k) * A232690(k) * A232690(n-k).