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

0,3

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.

Example

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) +...

Prog

(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), ", "))

Crossrefs

Cf. A186737, A227619.

Sequence in context: A005415 A371523 A219868 * A371575 A253571 A111686

Adjacent sequences: A224882 A224883 A224884 * A224886 A224887 A224888

Keyword

nonn

Author

Paul D. Hanna, Aug 22 2013

Status

approved