A271746 Number of set partitions of [n] such that 7 is the largest element of the last block.

406, 1145, 3627, 12521, 46299, 181265, 745107, 3195161, 14220459, 65412065, 309878787, 1507297001, 7508078619, 38208764465, 198238593267, 1046593626041, 5612793712779, 30528112814465, 168152752952547, 936705967782281, 5270538854994939, 29919810501018065

Offset

7,1

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).

Formula

G.f.: x^7*(720*x^6-122388*x^5+235852*x^4-161681*x^3+50632*x^2-7381*x+406) / Product_{j=1..6} (j*x-1).

From Colin Barker, Jan 04 2018: (Start)

a(n) = 32 + 121*2^(n-7) + 155*3^(n-7) + 5*4^(n-5) + 16*5^(n-7) + 6^(n-7) for n>7.

a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6) for n>13.

(End)

Mathematica

LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {406, 1145, 3627, 12521, 46299, 181265, 745107}, 30] (* Harvey P. Dale, Jun 12 2022 *)

Prog

(PARI) Vec(x^7*(406 - 7381*x + 50632*x^2 - 161681*x^3 + 235852*x^4 - 122388*x^5 + 720*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)) + O(x^40)) \\ Colin Barker, Jan 04 2018

Crossrefs

Column k=7 of A271466.

Sequence in context: A132362 A371900 A348185 * A203944 A203937 A203714

Adjacent sequences: A271743 A271744 A271745 * A271747 A271748 A271749

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 13 2016

Status

approved