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

104, 250, 692, 2110, 6932, 24190, 88772, 340030, 1351412, 5546110, 23407652, 101247550, 447454292, 2015029630, 9224364932, 42832260670, 201341787572, 956443162750, 4584181712612, 22137843427390, 107584138943252, 525581866073470, 2578798342362692

Offset: 6

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Crossrefs

Column k=6 of A271466.

Programs

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

Mathematica

Join[{104}, LinearRecurrence[{15, -85, 225, -274, 120}, {250, 692, 2110, 6932, 24190}, 30]] (* Vincenzo Librandi, Apr 14 2016 *)

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

Formula

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).

From Colin Barker, Jan 04 2018: (Start)

a(n) = 16 + 5*2^(n-3) + 35*3^(n-6) + 11*4^(n-6) + 5^(n-6) for n>6.

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.

(End)