cp's OEIS Frontend

A271745 Number of set partitions of [n] such that 6 is the largest element of the last block.

%I A271745 #14 Sep 08 2022 08:46:16
%S A271745 104,250,692,2110,6932,24190,88772,340030,1351412,5546110,23407652,
%T A271745 101247550,447454292,2015029630,9224364932,42832260670,201341787572,
%U A271745 956443162750,4584181712612,22137843427390,107584138943252,525581866073470,2578798342362692
%N A271745 Number of set partitions of [n] such that 6 is the largest element of the last block.
%H A271745 Alois P. Heinz, <a href="/A271745/b271745.txt">Table of n, a(n) for n = 6..1000</a>
%H A271745 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A271745 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F A271745 G.f.: 2*x^6*(60*x^5-3174*x^4+5210*x^3-2891*x^2+655*x-52) / Product_{j=1..5} (j*x-1).
%F A271745 From _Colin Barker_, Jan 04 2018: (Start)
%F A271745 a(n) = 16 + 5*2^(n-3) + 35*3^(n-6) + 11*4^(n-6) + 5^(n-6) for n>6.
%F A271745 a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5) for n>11.
%F A271745 (End)
%t A271745 Join[{104}, LinearRecurrence[{15, -85, 225, -274, 120}, {250, 692, 2110, 6932, 24190}, 30]] (* _Vincenzo Librandi_, Apr 14 2016 *)
%o A271745 (Magma) I:=[104,250,692,2110,6932,24190]; [n le 6 select I[n] else 15*Self(n-1)-85*Self(n-2)+225*Self(n-3)-274*Self(n-4)+120*Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Apr 14 2016
%o A271745 (PARI) x='x+O('x^99); Vec(2*x^6*(60*x^5-3174*x^4+5210*x^3-2891*x^2+655*x-52) / (120*x^5-274*x^4+225*x^3-85*x^2+15*x-1)) \\ _Altug Alkan_, Apr 14 2016
%Y A271745 Column k=6 of A271466.
%K A271745 nonn,easy
%O A271745 6,1
%A A271745 _Alois P. Heinz_, Apr 13 2016