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

%I A271748 #9 Jan 05 2018 09:08:42
%S A271748 8280,29874,117488,495408,2215148,10419024,51235748,262138728,
%T A271748 1389893708,7611839904,42937377908,248865777048,1478955826268,
%U A271748 8994703967184,55889046456068,354251342263368,2287372272350828,15026157296580864,100307242528430228,679694909468957688
%N A271748 Number of set partitions of [n] such that 9 is the largest element of the last block.
%H A271748 Alois P. Heinz, <a href="/A271748/b271748.txt">Table of n, a(n) for n = 9..1000</a>
%H A271748 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A271748 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).
%F A271748 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).
%F A271748 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
%o A271748 (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
%Y A271748 Column k=9 of A271466.
%K A271748 nonn,easy
%O A271748 9,1
%A A271748 _Alois P. Heinz_, Apr 13 2016