A179853 E.g.f. A(x) = Sum_{n>=0} a(n)*x^(3n)/(3n)!.

1, 6, 1080, 967680, 2494800000, 14122883174400, 149450965100236800, 2657377766797737984000, 73600830148552343949312000, 3000680514334863360000000000000, 172357905733383653098084542873600000, 13469219468410593291134233865512550400000

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

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

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

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

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

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

Mathematica

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

Prog

(PARI)
a(n) = (n+1)^(n-1)*(3*n)!/n!;
for(n=0, 30, print1(a(n), ", "));

Crossrefs

Sequence in context: A282233 A125536 A003763 * A268043 A190351 A267071

Adjacent sequences: A179850 A179851 A179852 * A179854 A179855 A179856

Keyword

nonn

Author

Vladimir Kruchinin, Jan 11 2011

Extensions

More terms from Harvey P. Dale, Oct 19 2011

Status

approved