cp's OEIS Frontend

A109821 Column 11 of array illustrated in A089574 and related to A034261.

%I A109821 #21 Apr 25 2024 14:55:52
%S A109821 27,482,3855,20329,82346,277295,813738,2145712,5192450,11708366,
%T A109821 24881487,50269005,97217758,180966915,325691821,568823951,967074547,
%U A109821 1604701323,2604691419,4143692621,6471712062,9937820779,15023357512,22384420182,32905773076,47768686720
%N A109821 Column 11 of array illustrated in A089574 and related to A034261.
%H A109821 Georg Fischer, <a href="/A109821/b109821.txt">Table of n, a(n) for n = 0..1000</a>
%H A109821 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A109821 G.f.: 27 + 482*x -x^2*(3855 -29786*x +118759*x^2 -310071*x^3 +574122*x^4 -780978*x^5 +792535*x^6 -601009*x^7 +336759*x^8 -135622*x^9 +37194*x^10 -6228*x^11 +481*x^12) /(x-1)^13. - _R. J. Mathar_, Aug 28 2018
%e A109821 An examination of the relevant ordered Gaussian polynomials reveals the following distribution (beginning with partitions of length three):
%e A109821 1 10 15 1
%e A109821 6 52 180 216 28
%e A109821 12 114 530 1386 1547 266
%e A109821 18 168 880 3086 7007 7616 1554
%e A109821 therefore (by summing each row) this sequence begins
%e A109821 27
%e A109821 482
%e A109821 3855
%e A109821 20329
%t A109821 LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1}, {27,482, 3855,20329,82346,277295,813738,2145712,5192450,11708366,24881487, 50269005, 97217758,180966915,325691821}, 1001] (* _Georg Fischer_, Feb 28 2019 *)
%Y A109821 Cf. A034261, A109820.
%Y A109821 Cf. A000330 (column 2), A086602 (column 3), A089574 (column 4), A107600 (column 5), A107601 (column 6), A109125 (column 7), A109126 (column 8), A109820 (column 9), A108538 (column 10), A109821 (column 11), A110553 (column 12), A110624 (column 13).
%K A109821 nonn
%O A109821 0,1
%A A109821 _Alford Arnold_, Jul 18 2005
%E A109821 More terms from _R. J. Mathar_, Aug 28 2018