A370289 G.f.: exp( Sum_{k>=1} (3*k)! / (3 * k!^3) * x^k/k ).

1, 2, 17, 218, 3404, 59644, 1127009, 22459358, 465607137, 9951077822, 217885806069, 4865577707714, 110439841557271, 2541477749853474, 59175695924948799, 1391881305657110326, 33029403365321798388, 789910458837089959548, 19021760426584464824327, 460890588704491541298970

Offset: 0

Author

Vaclav Kotesovec, Feb 14 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A229452, A370288, A229451, A370293.

Programs

Mathematica

CoefficientList[Series[Exp[Sum[(3*k)!/(3*k!^3)*x^k/k, {k, 1, 20}]], {x, 0, 20}], x]
CoefficientList[Series[Exp[2*x*HypergeometricPFQ[{1, 1, 4/3, 5/3}, {2, 2, 2}, 27*x]], {x, 0, 20}], x]

Formula

G.f. A(x) = G(x)^(1/3), where G(x) is the g.f. for A229451.

G.f. A(x) = G(x)^2, where G(x) is the g.f. for A229452.

a(n) ~ c * 3^(3*n) / n^2, where c = 8 * 3^(1/2) * Pi * A370293^2 = 0.104583575...