A370288 G.f.: exp( Sum_{k>=1} (3*k)! / (2 * k!^3) * x^k/k ).

1, 3, 27, 352, 5529, 97092, 1835873, 36585987, 758230146, 16197642704, 354473912751, 7911445710438, 179479850071287, 4128118899341085, 96071630789136060, 2258659897520722978, 53574405946963574691, 1280717656016739805269, 30828724750464602060491, 746692595857870177801332

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, A370289, A229451, A370293.

Programs

Mathematica

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

Formula

G.f. A(x) = G(x)^(1/2), where G(x) is the g.f. for A229451.

G.f. A(x) = G(x)^3, where G(x) is the g.f. for A229452.

a(n) ~ c * 3^(3*n) / n^2, where c = 144 * Pi^2 * A370293^3 = 0.167361952...