A370288 - OEIS

%I #9 Feb 14 2024 07:50:01

%S 1,3,27,352,5529,97092,1835873,36585987,758230146,16197642704,

%T 354473912751,7911445710438,179479850071287,4128118899341085,

%U 96071630789136060,2258659897520722978,53574405946963574691,1280717656016739805269,30828724750464602060491,746692595857870177801332

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

%H Vaclav Kotesovec, <a href="/A370288/b370288.txt">Table of n, a(n) for n = 0..700</a>

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

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

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

%t CoefficientList[Series[Exp[Sum[(3*k)!/(2*k!^3)*x^k/k, {k, 1, 20}]], {x, 0, 20}], x]

%t CoefficientList[Series[Exp[3*x*HypergeometricPFQ[{1, 1, 4/3, 5/3}, {2, 2, 2}, 27*x]], {x, 0, 20}], x]

%Y Cf. A229452, A370289, A229451, A370293.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 14 2024