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

30, 59, 139, 365, 1039, 3149, 10039, 33365, 114799, 406589, 1475239, 5460965, 20550559, 78375629, 302129239, 1174610165, 4597146319, 18085554269, 71434828039, 283020552965, 1123932750079, 4471296246509, 17811907987639, 71027855481365, 283452201569839

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Formula

G.f.: x^5*(24*x^4-460*x^3+599*x^2-241*x+30)/Product_{j=1..4} (j*x-1).

From Colin Barker, Dec 24 2017: (Start)

a(n) = 8 + 13*2^(n-5) + 7*3^(n-5) + 4^(n-5) for n>5.

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n>9.

(End)

Mathematica

Join[{30}, LinearRecurrence[{10, -35, 50, -24}, {59, 139, 365, 1039}, 30]] (* Vincenzo Librandi, Apr 13 2016 *)

Prog

(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
(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

Crossrefs

Column k=5 of A271466.

Sequence in context: A248572 A248739 A004962 * A121960 A040870 A356176

Adjacent sequences: A271741 A271742 A271743 * A271745 A271746 A271747

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 13 2016

Status

approved