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 A109125 #18 Aug 21 2024 18:00:49
%S A109125 2,41,292,1283,4253,11712,28261,61738,124763,236762,426557,735616,
%T A109125 1222064,1965563,3073176,4686337,6989056,10217495,14671058,20725145,
%U A109125 28845727,39605906,53704631,71987748,95471569,125369152,163119491
%N A109125 Column 7 of array illustrated in A089574 and related to A034261.
%H A109125 Harvey P. Dale, <a href="/A109125/b109125.txt">Table of n, a(n) for n = 0..1000</a>
%H A109125 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1). [From _R. J. Mathar_, Jun 26 2010]
%F A109125 From _R. J. Mathar_, Jun 26 2010: (Start)
%F A109125 a(n) = A105552(11+n,5+n).
%F A109125 G.f.: x*(-2-23*x+5*x^2+37*x^3-26*x^4-9*x^5+17*x^6-7*x^7+x^8)/(x-1)^9. a(n) = -1+1277*n/840 -19*n^3/480 -67*n^2/480 +41*n^5/80 +257*n^6/2800 +23*n^7/3360 +6049*n^4/5760 +n^8/5760. (End)
%e A109125 a(1) = 2 because 4+4+4 and 3+3+3+3 cannot be permuted. a(2) = 41 because there are 3 + 7 + 12 + 9 + 10 ways of permuting the associated partitions.
%e A109125 5553 (3 ways), 4441 & 544 (4+3 ways), 4432 (12 ways), 33331 & 4333 (5 + 4 ways) and 33322 (in 10 ways).
%t A109125 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{2,41,292,1283,4253,11712,28261,61738,124763},30] (* _Harvey P. Dale_, Aug 21 2024 *)
%Y A109125 Cf. A000124, A000330, A034261, A086602, A089574, A107601.
%K A109125 easy,nonn
%O A109125 0,1
%A A109125 _Alford Arnold_, Jun 19 2005
%E A109125 Extended beyond a(6) by _R. J. Mathar_, Jun 26 2010