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%I #8 Jan 05 2018 05:42:19
%S 42294,168509,724731,3321545,16075611,81602489,432156891,2377526345,
%T 13540170651,79588371929,481614364251,2993757491945,19079196017691,
%U 124446430190969,829494189346011,5642172217982345,39113680447384731,276028057609763609,1980851149371918171
%N Number of set partitions of [n] such that 10 is the largest element of the last block.
%H Alois P. Heinz, <a href="/A271749/b271749.txt">Table of n, a(n) for n = 10..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).
%F G.f.: x^10 *(362880*x^9 -4242318048*x^8 +10665532740*x^7 -10436766264*x^6 +5329525399*x^5 -1580780268*x^4 +282366820*x^3 -29937606*x^2 +1734721*x -42294) / Product_{j=1..9} (j*x-1).
%F 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
%o (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
%Y Column k=10 of A271466.
%K nonn,easy
%O 10,1
%A _Alois P. Heinz_, Apr 13 2016
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