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 A000497 M5186 N2254 #36 Jun 09 2018 09:20:27
%S A000497 1,25,490,9450,190575,4099095,94594500,2343240900,62199262125,
%T A000497 1764494857125,53338158823950,1712934942468750,58274046742786875,
%U A000497 2094379201311271875,79318164037837725000,3157886388887074845000
%N A000497 S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind.
%D A000497 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
%D A000497 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 296.
%D A000497 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000497 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000497 Vincenzo Librandi, <a href="/A000497/b000497.txt">Table of n, a(n) for n = 1..100</a>
%H A000497 H. W. Gould, Harris Kwong, Jocelyn Quaintance, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kwong/kwong9.html">On Certain Sums of Stirling Numbers with Binomial Coefficients</a>, J. Integer Sequences, 18 (2015), #15.9.6.
%H A000497 M. Ward, <a href="http://www.jstor.org/stable/2370916">The representations of Stirling's numbers and Stirling's polynomials as sums of factorials</a>, Amer. J. Math., 56 (1934), p. 87-95.
%F A000497 G.f.: x*(4*x+1)*hypergeom([3, 7/2],[],2*x)+28*x^3*hypergeom([4, 9/2],[],2*x). - _Mark van Hoeij_, Apr 07 2013
%F A000497 a(n) = n*(n+1)*(2*n+1)*2^n*GAMMA(n+3/2)/(9*sqrt(Pi)). - _Vaclav Kotesovec_, Aug 07 2013
%F A000497 (2*n-1)*(n-1)*a(n) -(n+1)*(1+2*n)^2*a(n-1)=0. - _R. J. Mathar_, Jun 09 2018
%p A000497 gf := (u,t)->exp(u*(exp(t)-1-t)); S2a := j->simplify(subs(u=0,t=0,diff(gf(u,t),u$j,t$(2*j+2)))/j!); for i from 1 to 20 do S2a(i); od;
%p A000497 # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 12 2000
%t A000497 t[n_, k_] := Sum[ (-1)^i*Binomial[n, i]*Sum[ (-1)^j*(k-i-j)^(n-i)/(j!*(k-i-j)!), {j, 0, k-i}], {i, 0, k}]; Table[ t[2n+2, n], {n, 1, 16} ](* _Jean-François Alcover_, Feb 24 2012 *)
%t A000497 Table[n*(n+1)*(2*n+1)*2^n*Gamma[n+3/2]/(9*Sqrt[Pi]),{n,1,20}] (* _Vaclav Kotesovec_, Aug 07 2013 *)
%Y A000497 Cf. A008299, A000504.
%K A000497 nonn,nice,easy
%O A000497 1,2
%A A000497 _N. J. A. Sloane_
%E A000497 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 12 2000