# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a343787 Showing 1-1 of 1 %I A343787 #7 Apr 29 2021 18:49:11 %S A343787 1,1,3,13,74,531,4563,45753,524345,6760039,96837333,1525909903, %T A343787 26230304235,488472319271,9796281435125,210496933103743, %U A343787 4824574494068495,117490079786298641,3029472152485535343,82454398253005541089,2362311059301928969755,71063998308414194250901 %N A343787 Number of ordered partitions of an n-set without blocks of size 4. %F A343787 E.g.f.: 1 / (2 + x^4/4! - exp(x)). %p A343787 a:= proc(n) option remember; `if`(n=0, 1, add( %p A343787 `if`(j=4, 0, a(n-j)*binomial(n, j)), j=1..n)) %p A343787 end: %p A343787 seq(a(n), n=0..21); # _Alois P. Heinz_, Apr 29 2021 %t A343787 nmax = 21; CoefficientList[Series[1/(2 + x^4/4! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]! %t A343787 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}] %Y A343787 Cf. A000670, A032032, A337058, A337059, A343664, A343788, A343789, A343790, A343791, A343792, A343793. %K A343787 nonn %O A343787 0,3 %A A343787 _Ilya Gutkovskiy_, Apr 29 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE