A316748 - OEIS

%I #11 May 21 2022 08:30:28

%S 1,6,726,365046,481183926,1312473466806,6422019989033526,

%T 51225575261701080246,621880652519326246083126,

%U 10911229213845806303174823606,265743324574322126992546955062326,8697919110119969555113124407898635446,372566878251517048881238923757823056246326

%N Stirling transform of (3*n)!.

%H Seiichi Manyama, <a href="/A316748/b316748.txt">Table of n, a(n) for n = 0..149</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>.

%F a(n) ~ (3*n)!.

%F a(n) ~ sqrt(2*Pi) * 3^(3*n + 1/2) * n^(3*n + 1/2) / exp(3*n).

%F E.g.f.: Sum_{k>=0} (3*k)! * (exp(x) - 1)^k / k!. - _Seiichi Manyama_, May 21 2022

%t Table[Sum[StirlingS2[n, k]*(3*k)!, {k, 0, n}], {n, 0, 15}]

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*(exp(x)-1)^k/k!))) \\ _Seiichi Manyama_, May 21 2022

%Y Cf. A000670, A064618, A316747, A353774.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jul 12 2018