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

0,2

Links

Table of n, a(n) for n=0..20.

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).

Example

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

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]!

Prog

(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), ", "))

Crossrefs

Cf. A232690.

Sequence in context: A127116 A107404 A120574 * A178324 A002710 A132609

Adjacent sequences: A333041 A333042 A333043 * A333045 A333046 A333047

Keyword

nonn

Author

Vaclav Kotesovec, Mar 06 2020

Status

approved