A356608 - OEIS

%I #26 Sep 14 2022 09:34:30

%S 1,1,1,1,1,6,31,106,281,1261,13861,106261,558361,2709136,32802771,

%T 447762316,4093711441,28011714641,293624974441,5549250905281,

%U 80454378591121,815886496908946,8379058314620071,168672787637953446,3514729162490432041,51656083670790267901

%N a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(24^k * (n - 4*k)!).

%H Vaclav Kotesovec, <a href="/A356608/b356608.txt">Table of n, a(n) for n = 0..455</a>

%F E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^4/24)).

%t a[n_] := n! * Sum[(n - 4*k)^k/(24^k*(n - 4*k)!), {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 26, 0] (* _Amiram Eldar_, Aug 19 2022 *)

%o (PARI) a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(24^k*(n-4*k)!));

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^4/24)))))

%Y Cf. A354436, A356029, A356328.

%Y Cf. A354552, A356630, A356634.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Aug 18 2022