A357174 - OEIS

%I #12 Sep 16 2022 11:46:28

%S 1,1,4,27,280,5045,134136,4269223,153188176,6657007113,371930499280,

%T 25072409219891,1872319689314856,154583203638018493,

%U 14784597239881491400,1641532369038107170815,201617558936011146124576,26755058016106471234608017

%N a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^n/(n - 3*k)!.

%F E.g.f.: Sum_{k>=0} (k * x)^k / (k! * (1 - (k * x)^3)).

%t a[n_] := n! * Sum[(n - 3*k)^n/(n - 3*k)!, {k, 0, Floor[n/3]} ]; a[0] = 1; Array[a, 18, 0] (* _Amiram Eldar_, Sep 16 2022 *)

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^k/(k!*(1-(k*x)^3)))))

%Y Cf. A256016, A356834.

%Y Cf. A353015, A357147.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 16 2022