A343790 - OEIS

%I #7 Apr 29 2021 20:09:10

%S 1,1,3,13,75,541,4683,47292,545819,7086973,102242283,1622530933,

%T 28089498891,526813752973,10640325166227,230258631645913,

%U 5315029292965675,130353994525735677,3385061859378821547,92787606222541942477,2677254928352340708075,81110818086045534369661

%N Number of ordered partitions of an n-set without blocks of size 7.

%F E.g.f.: 1 / (2 + x^7/7! - exp(x)).

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

%p       `if`(j=7, 0, a(n-j)*binomial(n, j)), j=1..n))

%p     end:

%p seq(a(n), n=0..21);  # _Alois P. Heinz_, Apr 29 2021

%t nmax = 21; CoefficientList[Series[1/(2 + x^7/7! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!

%t a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 7, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

%Y Cf. A000670, A032032, A337058, A337059, A343667, A343787, A343788, A343789, A343791, A343792, A343793.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 29 2021