A370055 a(n) = 3*(3*n+2)!/(2*n+3)!.
1, 3, 24, 330, 6552, 171360, 5581440, 218045520, 9945936000, 519177859200, 30535045632000, 1998518736614400, 144098325316915200, 11350405033583616000, 969837188805041356800, 89351761457237190912000, 8830056426362263572480000, 931769828125956695715840000
Offset: 0
Keywords
Programs
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PARI
a(n) = 3*(3*n+2)!/(2*n+3)!;
Formula
E.g.f.: exp( Sum_{k>=1} binomial(3*k,k) * x^k/k ).
a(n) = 3*A076151(n+1) for n > 0.
From Seiichi Manyama, Aug 31 2024: (Start)
E.g.f. satisfies A(x) = 1/(1 - x*A(x)^(2/3))^3.
a(n) = 3 * Sum_{k=0..n} (2*n+3)^(k-1) * |Stirling1(n,k)|. (End)
E.g.f.: (1/x) * Series_Reversion( x/(1 + x)^3 ). - Seiichi Manyama, Feb 06 2025