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 ).
1, 1, 3, 17, 144, 1647, 24037, 429483, 9088749, 221942779, 6130801041, 188708846991, 6398116247554, 236786117903526, 9495515095867953, 410104221125229354, 18977504682428845671, 936731766873748776822, 49127713187418767376060, 2728178479576867266738579, 159924801506251429348644138, 9868564065320443974954599471
Offset: 0
Keywords
Examples
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 + ... such that 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 + ... more explicitly, 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 + ...
Programs
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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]} for(n=0,30,print1(a(n),", "))