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

6,1

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).

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)

Mathematica

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

Prog

(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
(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

Crossrefs

Column k=6 of A271466.

Sequence in context: A258549 A121962 A235011 * A046298 A298325 A258556

Adjacent sequences: A271742 A271743 A271744 * A271746 A271747 A271748

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 13 2016

Status

approved