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

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

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).

Crossrefs

Column k=7 of A271466.

Programs

Mathematica

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

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

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)