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A271744 Number of set partitions of [n] such that 5 is the largest element of the last block.

%I A271744 #13 Sep 08 2022 08:46:16
%S A271744 30,59,139,365,1039,3149,10039,33365,114799,406589,1475239,5460965,
%T A271744 20550559,78375629,302129239,1174610165,4597146319,18085554269,
%U A271744 71434828039,283020552965,1123932750079,4471296246509,17811907987639,71027855481365,283452201569839
%N A271744 Number of set partitions of [n] such that 5 is the largest element of the last block.
%H A271744 Alois P. Heinz, <a href="/A271744/b271744.txt">Table of n, a(n) for n = 5..1000</a>
%H A271744 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A271744 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A271744 G.f.: x^5*(24*x^4-460*x^3+599*x^2-241*x+30)/Product_{j=1..4} (j*x-1).
%F A271744 From _Colin Barker_, Dec 24 2017: (Start)
%F A271744 a(n) = 8 + 13*2^(n-5) + 7*3^(n-5) + 4^(n-5) for n>5.
%F A271744 a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n>9.
%F A271744 (End)
%t A271744 Join[{30}, LinearRecurrence[{10, -35, 50, -24}, {59, 139, 365, 1039}, 30]] (* _Vincenzo Librandi_, Apr 13 2016 *)
%o A271744 (Magma) I:=[30,59,139,365,1039]; [n le 5 select I[n] else 10*Self(n-1)-35*Self(n-2)+50*Self(n-3)-24*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 13 2016
%o A271744 (PARI) Vec(x^5*(30 - 241*x + 599*x^2 - 460*x^3 + 24*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) + O(x^40)) \\ _Colin Barker_, Dec 24 2017
%Y A271744 Column k=5 of A271466.
%K A271744 nonn,easy
%O A271744 5,1
%A A271744 _Alois P. Heinz_, Apr 13 2016