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 A092255 #40 Sep 16 2017 21:15:57
%S A092255 1,1,3,10,23,66,222,561,1647,5410,14318,42351,137018,372191,1105275,
%T A092255 3537540,9772767,29090826,92364198,258208671,769820418,2429091885,
%U A092255 6850744365,20447143866,64200928194,182303186391,544550917797,1702925802766,4861918919447
%N A092255 a(0) = 1; for n > 0, a(n) = b(n) - n*b(n-1), b() = A076177().
%C A092255 For n>=1, a(n) mod 2 = A010060(n) the Thue-Morse sequence - _Benoit Cloitre_, Mar 22 2004
%C A092255 Number of ternary words of length n in which count(0's) <= count(1's) <= count(2's). a(2) = 3: words 12 and 21 with counts (0,1,1) and 22 with counts (0,0,2). - _David Scambler_, Aug 06 2012
%H A092255 Alois P. Heinz, <a href="/A092255/b092255.txt">Table of n, a(n) for n = 0..1000</a>
%F A092255 a(n) = n!*sum(i+j+k=n, 1/(i!*j!*k!)) (0<=k<=j<=i<=n). - _Benoit Cloitre_, Mar 22 2004
%F A092255 Recurrence: (n-3)*(n-1)*n^2*(63*n^3-561*n^2+1556*n-1343)*a(n) = (n-1)^2*(315*n^5 - 4065*n^4 + 19720*n^3 - 44240*n^2 + 44790*n - 15768)*a(n-1) - 3*(63*n^4 - 813*n^3 + 3392*n^2 - 5091*n + 2241)*(n-2)^3*a(n-2) + 9*(n-3)*(126*n^5 - 1311*n^4 + 4801*n^3 - 7677*n^2 + 5409*n - 1464)*(n-2)*a(n-3) - 27*(n-3)*(315*n^5 - 4065*n^4 + 19720*n^3 - 44240*n^2 + 44790*n - 15768)*(n-2)*a(n-4) + 81*(n-4)*(n-3)*(63*n^4 - 813*n^3 + 3392*n^2 - 5091*n + 2241)*(n-2)*a(n-5) + 243*(n-5)*(n-4)*(n-3)*(63*n^3-372*n^2+623*n-285)*(n-2)*a(n-6). - _Vaclav Kotesovec_, Jun 30 2013
%F A092255 a(n) ~ 1/2 * 3^(n-1) * (1 + 3/(2*sqrt(Pi*n/3)) + sqrt(3)*(1+2*cos(2*Pi*n/3))/(Pi*n)). - _Vaclav Kotesovec_, Mar 07 2014
%p A092255 a:= n-> n! *add(add(1/(k!*j!*(n-k-j)!), j=k..(n-k)/2), k=0..n/3):
%p A092255 seq(a(n), n=0..40); # _Alois P. Heinz_, Aug 07 2012
%t A092255 CoefficientList[Series[(HypergeometricPFQ[{},{},x]^3 + 3*HypergeometricPFQ[{},{},x]*HypergeometricPFQ[{},{1},x^2] + 2*HypergeometricPFQ[{},{1,1},x^3])/6,{x,0,30}],x]*Range[0,30]! (* _Vaclav Kotesovec_, Jul 01 2013 *)
%o A092255 (PARI) a(n)=sum(i=0,n,sum(j=0,i,sum(k=0,j,if(i+j+k-n,0,n!/i!/j!/k!))))
%Y A092255 Column k=3 of A226873. - _Alois P. Heinz_, Jun 21 2013
%K A092255 nonn
%O A092255 0,3
%A A092255 _N. J. A. Sloane_, Feb 20 2004
%E A092255 More terms from _Benoit Cloitre_, Mar 22 2004