A179853 - OEIS

%I #21 Oct 29 2022 09:34:02

%S 1,6,1080,967680,2494800000,14122883174400,149450965100236800,

%T 2657377766797737984000,73600830148552343949312000,

%U 3000680514334863360000000000000,172357905733383653098084542873600000,13469219468410593291134233865512550400000

%N E.g.f. A(x) = Sum_{n>=0} a(n)*x^(3n)/(3n)!.

%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

%F a(n) = (n+1)^(n-1)*(3*n)!/n!.

%F E.g.f. A(x) satisfies A(x) = Sum_{n>=0} a(n)*x^(3*n)/(3n)!

%F This is the special case m=3 of the following:

%F The e.g.f. A(x) = Sum_{n>=0} a(n)*x^(m*n)/(m*n)! satisfies A(x) = exp(x^m*A(x))

%F (and the corresponding terms are a(n) = (n+1)^(n-1)*(m*n)!/n!).

%t Table[(n+1)^(n-1)(3n)!/n!,{n,0,20}] (* _Harvey P. Dale_, Oct 19 2011 *)

%o (PARI)

%o a(n) = (n+1)^(n-1)*(3*n)!/n!;

%o for(n=0,30,print1(a(n),", "));

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Jan 11 2011

%E More terms from _Harvey P. Dale_, Oct 19 2011