A271749 Number of set partitions of [n] such that 10 is the largest element of the last block.

42294, 168509, 724731, 3321545, 16075611, 81602489, 432156891, 2377526345, 13540170651, 79588371929, 481614364251, 2993757491945, 19079196017691, 124446430190969, 829494189346011, 5642172217982345, 39113680447384731, 276028057609763609, 1980851149371918171

Offset: 10

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).

Crossrefs

Column k=10 of A271466.

Programs

PARI

Vec(x^10*(42294 - 1734721*x + 29937606*x^2 - 282366820*x^3 + 1580780268*x^4 - 5329525399*x^5 + 10436766264*x^6 - 10665532740*x^7 + 4242318048*x^8 - 362880*x^9) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)*(1 - 9*x)) + O(x^40)) \\ Colin Barker, Jan 05 2018

Formula

G.f.: x^10 *(362880*x^9 -4242318048*x^8 [phone]*x^7 -10436766264*x^6 [phone]*x^5 -1580780268*x^4 [phone]*x^3 -29937606*x^2 +1734721*x -42294) / Product_{j=1..9} (j*x-1).

a(n) = 45*a(n-1) - 870*a(n-2) + 9450*a(n-3) - 63273*a(n-4) + 269325*a(n-5) - 723680*a(n-6) + 1172700*a(n-7) - 1026576*a(n-8) + 362880*a(n-9) for n>19. - Colin Barker, Jan 05 2018