OFFSET
0,3
COMMENTS
Compare to the e.g.f. of A002105, the reduced tangent numbers:
Sum_{n>=0} Product_{k=1..n} tanh(k*x).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..140
FORMULA
a(n) ~ c * d^n * (n!)^3 / sqrt(n), where d = 2.67441747301630303932685879..., c = 0.4405132627693901422580367... . - Vaclav Kotesovec, Nov 02 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + 16*x^2/2! + 970*x^3/3! + 146176*x^4/4! +...
where
A(x) = 1 + tanh(x) + tanh(2*1*x)*tanh(2*2*x) + tanh(3*1*x)*tanh(3*2*x)*tanh(3*3*x) + tanh(4*1*x)*tanh(4*2*x)*tanh(4*3*x)*tanh(4*4*x) +...
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Sum[Product[Tanh[n*k*x], {k, n}], {n, 0, nn}], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 26 2024 *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, tanh(m*k*X))); n!*polcoeff(Egf, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 06 2013
STATUS
approved