A196194 E.g.f.: 1 + Sum_{n>=1} x^n * Product_{k=1..n} (exp(k*x)-1)/(exp(x)-1).

1, 1, 4, 42, 804, 24200, 1052310, 62399232, 4838470280, 475205921136, 57651242228010, 8466308935131080, 1480085055633108012, 303741049766220682200, 72304996099042631680574, 19761618044081811015046320, 6145897155031392768635838480

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.

Formula

a(n) ~ 12^(n+1) * n^(2*n+1) / (exp(2*n) * Pi^(2*n+1)). - Vaclav Kotesovec, Nov 04 2014

Example

E.g.f.: A(x) = 1 + x + 4*x^2/2! + 42*x^3/3! + 804*x^4/4! + 24200*x^5/5! + ...
where
A(x) = 1 + x*(exp(x)-1)/(exp(x)-1) + x^2*(exp(x)-1)*(exp(2*x)-1)/(exp(x)-1)^2 + x^3*(exp(x)-1)*(exp(2*x)-1)*(exp(3*x)-1)/(exp(x)-1)^3 + ...
Equivalently,
A(x) = 1 + x + x^2*(exp(x)+1) + x^3*(exp(x)+1)*(exp(2*x)+exp(x)+1) + x^4*(exp(x)+1)*(exp(2*x)+exp(x)+1)*(exp(3*x)+exp(2*x)+exp(x)+1) + ...

Prog

(PARI) {a(n)=n!*polcoeff(1+sum(m=1, n, x^m*prod(k=1, m, (exp(k*x+x*O(x^n))-1)/(exp(x+x*O(x^n))-1))), n)}

Crossrefs

Cf. A196193.

Sequence in context: A268567 A197866 A197948 * A197323 A197976 A338194

Adjacent sequences: A196191 A196192 A196193 * A196195 A196196 A196197

Keyword

nonn

Author

Paul D. Hanna, Sep 28 2011

Status

approved