A370294 G.f.: exp(Sum_{k>=1} (4*k)!/(4!*k!^4) * x^k/k).

1, 1, 53, 5186, 663444, 98703235, 16179000550, 2837251240021, 522937525075783, 100134345595461824, 19762585810520535829, 3997199042964419204924, 825055790810846248226675, 173231819660726985218760834, 36906136513918240767383588700, 7962139696794640558535530147729

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

G.f. A(x) = G(x)^(1/24), where G(x) is the g.f. for A333042.

a(n) ~ c * 4^(4*n)/n^(5/2), where c = exp(HypergeometricPFQ[{1, 1, 5/4, 3/2, 7/4}, {2, 2, 2, 2}, 1] / 256) / (24*sqrt(2)*Pi^(3/2)) = 0.005320414767134132512371690902604699480645296829596277834542636529157577...

Mathematica

CoefficientList[Series[Exp[Sum[(4*k)!/(4!*k!^4)*x^k/k, {k, 1, 20}]], {x, 0, 20}], x]
CoefficientList[Series[Exp[x*HypergeometricPFQ[{1, 1, 5/4, 3/2, 7/4}, {2, 2, 2, 2}, 256*x]], {x, 0, 20}], x]

Crossrefs

Cf. A008977, A082368, A229452, A370295, A333042.

Sequence in context: A013542 A200917 A234630 * A088784 A104820 A093253

Adjacent sequences: A370291 A370292 A370293 * A370295 A370296 A370297

Keyword

nonn

Author

Vaclav Kotesovec, Feb 14 2024

Status

approved