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 A120759 #8 Jun 13 2015 15:34:36
%S A120759 1,2,5,24,527,271156,73452582161,5395271857717411958088,
%T A120759 29108958418479344853405820427519529324955406,
%U A120759 847331460208759521535495911124086692972161538057881358236684093384849875943910959287454
%N A120759 Eigensequence for subpartitions of a partition.
%C A120759 Let this sequence, A, be a partition P=A, then the total number of subpartitions of the partition P is equal to A. See A115728 for the definition of subpartitions of a partition.
%F A120759 a(n) = a(n-1)^2 + 1 - Sum_{k=0..n-2} (-1)^(n-k)*a(k)*C(a(k),n-k) for n>=1, with a(0)=1.
%F A120759 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n*(1-x)^a(n).
%e A120759 At n=4, the recurrence gives:
%e A120759 a(4) = a(3)^2 + 1 - Sum_{k=0..2} (-1)^(4-k)*a(k)*C(a(k),4-k)
%e A120759 = a(3)^2 + 1 - [a(0)*C(a(0),4) - a(1)*C(a(1),3) + a(2)*C(a(2),2)]
%e A120759 = 24^2 + 1 - [1*0 - 2*0 + 5*C(5,2)] = 24^2 + 1 - 5*10 = 527.
%e A120759 The recurrence extracts a(n) from the g.f.:
%e A120759 1/(1-x) = 1*(1-x) + 2*x*(1-x)^2 + 5*x^2*(1-x)^5 + 24*x^3*(1-x)^24 +...
%e A120759 + a(n)*x^n*(1-x)^a(n) +...
%e A120759 The number of digits of a(n) base 10 begins:
%e A120759 [1,1,1,2,3,6,11,22,44,87,174,348,696,1391,...]
%o A120759 (PARI) a(n)=if(n==0,1,a(n-1)^2+1-sum(k=0,n-2,(-1)^(n-k)*a(k)*binomial(a(k),n-k)))
%o A120759 (PARI) a(n)=polcoeff(x^n-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^a(k)), n)
%Y A120759 Cf. A115728.
%K A120759 eigen,nonn
%O A120759 0,2
%A A120759 _Franklin T. Adams-Watters_ and _Paul D. Hanna_, Jul 03 2006