A320761 - OEIS

%I #7 Dec 14 2020 05:13:40

%S 1,12,168,2464,38808,657972,11997216,234594360,4903616718,

%T 109205019924,2582909885556,64686057980544,1710536977653504,

%U 47637803779229664,1393903719674129664,42758329987344875904,1372254504736418142840,45989719374155059863360

%N Number of ordered set partitions of [n] where the maximal block size equals five.

%H Alois P. Heinz, <a href="/A320761/b320761.txt">Table of n, a(n) for n = 5..424</a>

%F E.g.f.: 1/(1-Sum_{i=1..5} x^i/i!) - 1/(1-Sum_{i=1..4} x^i/i!).

%F a(n) = A276925(n) - A276924(n).

%p b:= proc(n, k) option remember; `if`(n=0, 1, add(

%p       b(n-i, k)*binomial(n, i), i=1..min(n, k)))

%p     end:

%p a:= n-> (k-> b(n, k) -b(n, k-1))(5):

%p seq(a(n), n=5..25);

%t b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];

%t a[n_] := With[{k = 5}, b[n, k] - b[n, k-1]];

%t a /@ Range[5, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)

%Y Column k=5 of A276922.

%Y Cf. A276924, A276925.

%K nonn

%O 5,2

%A _Alois P. Heinz_, Oct 20 2018