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 A360036 #27 Aug 17 2025 12:49:11
%S A360036 0,0,0,6,24,100,360,1274,4368,14760,49200,162382,531432,1727180,
%T A360036 5580120,17936130,57395616,182948560,581130720,1840247318,5811307320,
%U A360036 18305618100,57531942600,180441092746,564859072944,1765184603000,5507375961360,17157594341214,53379182394888
%N A360036 Expansion of e.g.f. x*exp(x)*(sinh(x))^2.
%C A360036 a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets have an odd number of elements and an element is selected from the third.
%H A360036 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-7,-12,17,6,-9).
%F A360036 a(n) = n*A081251(n-2) for n >= 3.
%F A360036 a(n) = n*(3^(n-1) + (-1)^(n-1) - 2)/4.
%F A360036 G.f.: 2*x^3*(3 - 6*x - x^2)/((1 - x)^2*(1 + x)^2*(1 - 3*x)^2). - _Stefano Spezia_, Jan 23 2023
%e A360036 The first 4 cases are shown below for a(4)=24 (where the element selected from the third set is in parenthesis):
%e A360036 {1}, {2}, {(3), 4}
%e A360036 {1}, {2}, {3, (4)}
%e A360036 {2}, {1}, {(3), 4}
%e A360036 {2}, {1}, {3, (4)}.
%t A360036 With[{nn=30},CoefficientList[Series[x Exp[x]Sinh[x]^2,{x,0,nn}],x] Range[0,nn]!] (* or *) LinearRecurrence[{6,-7,-12,17,6,-9},{0,0,0,6,24,100},30] (* _Harvey P. Dale_, Aug 17 2025 *)
%Y A360036 Cf. A081251, A015518, A360023, A360035.
%K A360036 nonn,easy
%O A360036 0,4
%A A360036 _Enrique Navarrete_, Jan 22 2023