A351735 - OEIS

%I #11 May 21 2022 08:40:55

%S 1,0,6,27,324,4050,64962,1224720,26776656,665390376,18529576200,

%T 571602980520,19349098690248,713092338026640,28422424039182768,

%U 1218246132898693080,55876497505161154560,2730710993688989519040,141654212475516155694528

%N Expansion of e.g.f. 1/(1 - 3 * x)^x.

%F a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * |Stirling1(n-k,k)|/(n-k)!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^x))

%o (PARI) a(n) = n!*sum(k=0, n\2, 3^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!);

%Y Cf. A053490, A053491.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 20 2022