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

9,1

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).

Formula

G.f.: 2*x^9 *(20160*x^8 -51819984*x^7 +121981810*x^6 -109114599*x^5 +49449082*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

Prog

(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

Crossrefs

Column k=9 of A271466.

Sequence in context: A188101 A157731 A252581 * A064014 A203881 A145527

Adjacent sequences: A271745 A271746 A271747 * A271749 A271750 A271751

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 13 2016

Status

approved