A271748 Number of set partitions of [n] such that 9 is the largest element of the last block.

8280, 29874, 117488, 495408, 2215148, 10419024, 51235748, 262138728, 1389893708, 7611839904, 42937377908, 248865777048, 1478955826268, 8994703967184, 55889046456068, 354251342263368, 2287372272350828, 15026157296580864, 100307242528430228, 679694909468957688

Offset: 9

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

Crossrefs

Column k=9 of A271466.

Programs

PARI

Vec(2*x^9*(4140 - 134103*x + 1781452*x^2 - 12490518*x^3 + 49449082*x^4 - 109114599*x^5 + 121981810*x^6 - 51819984*x^7 + 20160*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)) + O(x^40)) \\ Colin Barker, Jan 05 2018

Formula

G.f.: 2*x^9 *(20160*x^8 -51819984*x^7 [phone]*x^6 -109114599*x^5 [phone]*x^4 -12490518*x^3 +1781452*x^2 -134103*x +4140) / Product_{j=1..8} (j*x-1).

a(n) = 36*a(n-1) - 546*a(n-2) + 4536*a(n-3) - 22449*a(n-4) + 67284*a(n-5) - 118124*a(n-6) + 109584*a(n-7) - 40320*a(n-8) for n>17. - Colin Barker, Jan 05 2018