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 A275872 #25 Aug 29 2016 00:58:29
%S A275872 0,0,1,1,2,6,18,54,173,605,2274,9020,37486,163128,743101,3535765,
%T A275872 17518018,90126158,480514430,2650912738,15112253425,88903779401,
%U A275872 539003066674,3363608949132,21581457167994,142227480847092,961868098767105,6669657795455817,47380035801732034,344555811578909254,2563218995058696890
%N A275872 A binomial convolution recurrence sequence.
%C A275872 Shifts 2 places left and decreases by one under a variant of binomial transform (see formula section).
%H A275872 Robert Israel, <a href="/A275872/b275872.txt">Table of n, a(n) for n = 0..648</a>
%F A275872 Sum_{i=0..n} binomial(n+1,i+1)*a(i) = a(n+2) - 1.
%F A275872 G.f. g(x) satisfies g(x) = x^2/(1-x) + x^2*g(x/(1-x))/(1-x)^2. - _Robert Israel_, Aug 28 2016
%p A275872 A[0]:= 0:
%p A275872 A[1]:= 0:
%p A275872 for m from 2 to 50 do
%p A275872 A[m]:= 1 + add(binomial(m-1,i+1)*A[i],i=0..m-2)
%p A275872 od:
%p A275872 seq(A[i],i=0..50); # _Robert Israel_, Aug 28 2016
%t A275872 Clear[a]; a[0] = 0 ; a[1] = 0; a[n_] := a[n] = 1 + Sum[Binomial[n - 1, j+1]*a[j], {j, 0, n - 1}]; Table[a[n], {n, 0, 22}]
%o A275872 (PARI) first(n)=my(v=vector(n)); for(k=0,n-2, v[k+2]=sum(i=2,k, binomial(k+1,i+1)*v[i])+1); concat(0,v) \\ _Charles R Greathouse IV_, Aug 29 2016
%Y A275872 Cf. A000994, A007476, A032346.
%K A275872 nonn,eigen,easy
%O A275872 0,5
%A A275872 _Olivier Gérard_, Aug 11 2016