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 A130408 #22 Sep 08 2022 08:45:30
%S A130408 1,1,-1,3,-44,49,-9895,3124,-54429,2624879,-59124785,163841201,
%T A130408 -2508904105349,1776678914237,-2029995134495,175211074573961,
%U A130408 -21557683580436716,94127808754677868,-87882971047931164843,161354083950193175137,-104683178840085862057001
%N A130408 Numerators of a-sequence for Sheffer matrix A130191 (Stirling2 squared).
%C A130408 The denominators are found in A130409.
%C A130408 From the definition of the a-sequence {r(n)} one has the recurrence for (Stirling2)^2 = S2sq: S2sq(n,m) = (n/m)*Sum_{j=0..n-m} binomial(m-1+j,j)*r(j)*S2sq(n-1,m-1+j), n >= m >= 1.
%C A130408 For the notion of the a-sequence for a Sheffer matrix see the W. Lang link under A006232. Here the a-sequence is called r(n) because it is a sequence of rationals.
%H A130408 G. C. Greubel, <a href="/A130408/b130408.txt">Table of n, a(n) for n = 0..250</a>
%H A130408 Wolfdieter Lang, <a href="/A130408/a130408.txt">Rationals and more. </a>
%F A130408 a(n) = numerator(r(n)), n >= 0, with the rational r(n) sequence with e.g.f. x/log(1+log(1+x)). {r(n)} is the a-sequence for the Sheffer matrix (Stirling2)^2 (A130191).
%e A130408 Rationals r(n): [1, 1, -1/3, 3/4, -44/15, 49/3, -9895/84, 3124/3, -54429/5, ...].
%e A130408 Recurrence for (Stirling2)^2: 32=S2sq(4,2) = (4/2)*(1*1*5 + 2*1*6 + 3*(-1/3)*1).
%p A130408 seq( numer( coeff(series( x/log(1+log(1+x)), x, n+2)*factorial(n), x, n) ), n = 0..20); # _G. C. Greubel_, Jan 26 2020
%t A130408 With[{m = 20}, CoefficientList[Series[x/Log[1+Log[1+x]], {x,0,m}], x]*Range[0, m]!]//Numerator (* _G. C. Greubel_, Jan 26 2020 *)
%o A130408 (Magma) m:=22; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( x/Log(1+Log(1+x)) )); [Numerator(Factorial(n-1)*b[n]): n in [1..m-1]]; // _G. C. Greubel_, Jan 26 2020
%o A130408 (Sage) [numerator( factorial(n)*( x/log(1+log(1+x)) ).series(x,n+1).list()[n]) for n in (0..20)] # _G. C. Greubel_, Jan 26 2020
%Y A130408 Cf. A006232(n)/A006233(n) (a-sequence for Stirling2 A048993).
%K A130408 sign,frac,easy
%O A130408 0,4
%A A130408 _Wolfdieter Lang_, Jun 01 2007