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 A326241 #13 Jun 02 2025 15:22:40
%S A326241 1,1,1,3,12,36,216,1296,10368,78912,634896,5572656,51817536,477672768,
%T A326241 8268884352,101752505856,1417554660096,20985416983296,344834432195328,
%U A326241 5096129755468032,70148917686998016
%N A326241 Number of degree-n even permutations of order dividing 12.
%D A326241 J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, Inc. New York, 1958 (Chap 4, Problem 22).
%H A326241 Robert Israel, <a href="/A326241/b326241.txt">Table of n, a(n) for n = 0..482</a>
%H A326241 Lev Glebsky, Melany Licón, Luis Manuel Rivera, <a href="https://arxiv.org/abs/1907.00548">On the number of even roots of permutations</a>, arXiv:1907.00548 [math.CO], 2019.
%F A326241 E.g.f.: (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) + (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)).
%e A326241 For n=3 the a(3)=3 solutions are (1), (1, 2, 3), (1, 3, 2) (permutations in cyclic notation).
%p A326241 E:= (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) + (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)):
%p A326241 S:= series(E,x,31):
%p A326241 seq(coeff(S,x,i)*i!,i=0..30);# _Robert Israel_, Jul 08 2019
%t A326241 With[{nn = 22}, CoefficientList[Series[1/2 Exp[x + x^2/2 + x^3/3 + x^4/4 + x^6/6 +x^12/12]+1/2 Exp[x - x^2/2 + x^3/3 - x^4/4 - x^6/6 - x^12/12], {x, 0, nn}], x]*Range[0, nn]!]
%Y A326241 Cf. A053502, A326242, A000704, A061130, A061131, A061132, A048099, A051695, A061133, A061134, A061135, A326242.
%K A326241 easy,nonn
%O A326241 0,4
%A A326241 _Luis Manuel Rivera Martínez_, Jul 06 2019