This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110553 #29 Aug 03 2025 05:01:16
%S A110553 9,284,3004,19078,88938,335612,1084387,3109060,8104089,19539904,
%T A110553 44141520,94346102,192252586,375787005,708083995,1291443529,
%U A110553 2287680232,3947261426,6650353141,10963787826,17719064134,28117822582,43872849975,67394593662,102035462287,152406906280
%N A110553 Column 12 of an array illustrated in A089584 and related to A034261.
%C A110553 The column sequences can also be calculated using sequences which map to associated partitions. For example, 4 32 132 392 ... maps to 5+5+5+4 (n=19) and sequence 5 50 245 840 ... maps to 4+4+4+4+3. Many partitions map to the same sequences since the mapping depends only on the "degree" of the partition. In the above two cases, the degrees are 31 and 41 respectively. At n = 20 the relevant degrees are: 21,31,211,311,22,221,42,212,321,24 and 61. The associated partitions can be permuted with the number of ways as indicated: 3 4 12 20 6 30 15 30 60 15 and 7 ways. Adding these values with the 32 and 50 ways from our first two sequences confirms that A110553(2) = 284.
%H A110553 Georg Fischer, <a href="/A110553/b110553.txt">Table of n, a(n) for n = 0..1000</a>
%H A110553 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A110553 G.f.: 9+284*x+3004*x^2 -x^3*(-19078 +178154*x -826578*x^2 +2465215*x^3 -5191980*x^4 +8073520*x^5 -9475220*x^6 +8461596*x^7 -5732830*x^8 +2904174*x^9 -1067563*x^10 +269335*x^11 -41760*x^12 +3003*x^13) /(x-1)^14. - _R. J. Mathar_, Aug 28 2018
%e A110553 An examination of the relevant ordered Gaussian polynomials reveals the following distributions:
%e A110553 5 4
%e A110553 7 120 120 34 3
%e A110553 112 1127 1190 470 96 9
%e A110553 882 6692 7147 3270 910 162 15
%e A110553 therefore the sequence begins
%e A110553 9
%e A110553 284
%e A110553 3004
%e A110553 19078
%e A110553 ...
%t A110553 LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1}, {9, 284, 3004,19078, 88938, 335612, 1084387, 3109060, 8104089,19539904, 44141520, 94346102, 192252586, 375787005, 708083995, 1291443529, 2287680232}, 1001] (* _Georg Fischer_, Feb 28 2019 *)
%Y A110553 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 A110553 nonn,easy
%O A110553 0,1
%A A110553 _Alford Arnold_, Jul 29 2005
%E A110553 More terms from _R. J. Mathar_, Aug 28 2018