A271747 Number of set partitions of [n] such that 8 is the largest element of the last block.

1754, 5649, 20085, 77133, 315597, 1362669, 6164685, 29058813, 142084077, 717966669, 3737612685, 19991467293, 109605434157, 614681711469, 3519553748685, 20540447808573, 121996580169837, 736352527581069, 4510823754140685, 28011087761890653, 176122939449075117

Offset: 8

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

Crossrefs

Column k=8 of A271466.

Programs

PARI

Vec(x^8*(1754 - 43463*x + 426701*x^2 - 2104109*x^3 + 5424029*x^4 - 6799268*x^5 + 3145476*x^6 - 5040*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)) + O(x^40)) \\ Colin Barker, Jan 04 2018

Formula

G.f.: x^8 *(5040*x^7 -3145476*x^6 +6799268*x^5 -5424029*x^4 +2104109*x^3 -426701*x^2 +43463*x -1754)/Product_{j=1..7} (j*x-1).

From Colin Barker, Jan 04 2018: (Start)

a(n) = 64 + 91*2^(n-6) + 245*2^(2*n-15) + 11*2^(n-7)*3^(n-8) + 217*3^(n-7) + 161*5^(n-8) + 7^(n-8) for n>8.

a(n) = 28*a(n-1) - 322*a(n-2) + 1960*a(n-3) - 6769*a(n-4) + 13132*a(n-5) - 13068*a(n-6) + 5040*a(n-7) for n>15.

(End)