|
| |
|
|
A194958
|
|
E.g.f. satisfies: A(x) = cosh(x) + x*A(x)^2.
|
|
2
|
|
|
|
1, 1, 5, 36, 409, 6280, 121501, 2839424, 77834737, 2449360512, 87040440181, 3447798906112, 150645874207753, 7197909122453504, 373365727806824845, 20895734364795187200, 1255062315134651501281, 80528111291313595580416, 5497183726333878664852453
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
The radius of convergence r of the e.g.f. A(x) satisfies: r = 1/(4*cosh(r)) = limit (n+1)*a(n)/a(n+1) = 0.24280736240... with A(r) = 1/(2*r) = 2.059245630...
|
|
|
LINKS
|
Table of n, a(n) for n=0..18.
|
|
|
FORMULA
|
E.g.f.: A(x) = (1 - sqrt(1 - 4*x*cosh(x))) / (2*x).
a(n) = (1 + (-1)^n)/2 + n*Sum_{k=0..n-1} C(n-1,k)*a(k)*a(n-1-k) for n>=0.
|
|
|
EXAMPLE
|
E.g.f.: A(x) = 1 + x + 5*x^2/2! + 36*x^3/3! + 409*x^4/4! + 6280*x^5/5! +...
Related expansion:
A(x)^2 = 1 + 2*x + 12*x^2/2! + 102*x^3/3! + 1256*x^4/4! + 20250*x^5/5! +...
|
|
|
PROG
|
(PARI) {a(n)=n!*polcoeff((1 - sqrt(1 - 4*x*cosh(x +O(x^(n+2))))) / (2*x), n)}
(PARI) {a(n)=(1 + (-1)^n)/2 +n*sum(k=0, n-1, binomial(n-1, k)*a(k)*a(n-1-k))}
|
|
|
CROSSREFS
|
Cf. A194957, A194471.
Sequence in context: A081918 A062024 A031971 * A132686 A118018 A156355
Adjacent sequences: A194955 A194956 A194957 * A194959 A194960 A194961
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul D. Hanna, Sep 06 2011
|
|
|
STATUS
|
approved
|
| |
|
|
