OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..100
FORMULA
E.g.f.: Sum_{n>=0} sinh(x)^n * Product_{k=0..n-1} cosh(2^k*x)^n.
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 10*x^3/3! + 152*x^4/4! + 3976*x^5/5! +...
where
A(x) = 1 + sinh(2*x)/2 + sinh(2^2*x)^2/2^4 + sinh(2^3*x)^3/2^9 + sinh(2^4*x)^4/2^16 +...
Also,
A(x) = 1 + sinh(x)*cosh(x) + sinh(x)^2*cosh(x)^2*cosh(2*x)^2 + sinh(x)^3*cosh(x)^3*cosh(2*x)^3*cosh(4*x)^3 + sinh(x)^4*cosh(x)^4*cosh(2*x)^4*cosh(4*x)^4*cosh(8*x)^4 +...
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sinh(2^m*X)^m/2^(m^2))); n!*polcoeff(A, n)}
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sinh(X)^m*prod(k=0, m-1, cosh(2^k*X)^m))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 12 2011
STATUS
approved