cp's OEIS Frontend

A298691 G.f. A(x) satisfies: A(x) = Sum_{n>=0} binomial( n*(n+1)/2, n) * x^n / A(x)^( n*(n-1)/2 ).

%I A298691 #3 Jan 24 2018 23:04:40
%S A298691 1,1,3,17,144,1647,24037,429483,9088749,221942779,6130801041,
%T A298691 188708846991,6398116247554,236786117903526,9495515095867953,
%U A298691 410104221125229354,18977504682428845671,936731766873748776822,49127713187418767376060,2728178479576867266738579,159924801506251429348644138,9868564065320443974954599471
%N A298691 G.f. A(x) satisfies: A(x) = Sum_{n>=0} binomial( n*(n+1)/2, n) * x^n / A(x)^( n*(n-1)/2 ).
%e A298691 G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 144*x^4 + 1647*x^5 + 24037*x^6 + 429483*x^7 + 9088749*x^8 + 221942779*x^9 + 6130801041*x^10 + 188708846991*x^11 + 6398116247554*x^12 + 236786117903526*x^13 + 9495515095867953*x^14 + 410104221125229354*x^15 + ...
%e A298691 such that
%e A298691 A(x) = 1 + C(1,1)*x + C(3,2)*x^2/A(x) + C(6,3)*x^3/A(x)^3 + C(10,4)*x^4/A(x)^6 + C(15,5)*x^5/A(x)^10 + C(21,6)*x^6/A(x)^15 + C(28,7)*x^7/A(x)^21 + ...
%e A298691 more explicitly,
%e A298691 A(x) = 1 + x + 3*x^2/A(x) + 20*x^3/A(x)^3 + 210*x^4/A(x)^6 + 3003*x^5/A(x)^10 + 54264*x^6/A(x)^15 + 1184040*x^7/A(x)^21 + 30260340*x^8/A(x)^28 + ...
%o A298691 (PARI) {a(n) = my(A=[1]); for(i=1,n, A = Vec(sum(m=0,#A,binomial(m*(m+1)/2,m) * x^m/Ser(A)^(m*(m-1)/2) ))); A[n+1]}
%o A298691 for(n=0,30,print1(a(n),", "))
%Y A298691 Cf. A014068, A298689, A298690.
%K A298691 nonn
%O A298691 0,3
%A A298691 _Paul D. Hanna_, Jan 24 2018