A224885 G.f.: A(x) = 1+x + Sum_{n>=2} Product_{k=1..n} (A(x)^k - 1).
1, 1, 2, 15, 143, 1552, 18282, 228174, 2976534, 40256580, 561755676, 8066942027, 119104886610, 1809118800204, 28327453520403, 458854209551159, 7727223037965079, 136130623466875012, 2526349854311842166, 49724570281877830993, 1043539871136604436514, 23417606258398828845811
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 143*x^4 + 1552*x^5 + 18282*x^6 +... where A(x) = 1+x + (A(x)-1)*(A(x)^2-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1)*(A(x)^4-1) + (A(x)-1)*(A(x)^2-1)*(A(x)^3-1)*(A(x)^4-1)*(A(x)^5-1) +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..125
- Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.
Programs
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PARI
{a(n)=local(A=1+x);for(i=1,n,A=1+x+sum(k=2,n,prod(j=1,k,A^j-1 +x*O(x^n))));polcoeff(A,n)} for(n=0,20,print1(a(n),", "))