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A162654
E.g.f. satisfies: A(x) = 1 + x*cosh(x*A(x)).
1
1, 1, 0, 3, 24, 65, 480, 8827, 72576, 657729, 13754880, 215578451, 2884992000, 62280478273, 1404449120256, 27032417472075, 640338738708480, 17729894860794497, 453894468727209984, 12438629293065953059
OFFSET
0,4
LINKS
FORMULA
a(n) = n!*Sum_{k=0..n} C(n-k+1,k)/(n-k+1) * Sum_{j=0..k} C(k,j)/2^k*(2j-k)^(n-k)/(n-k)!.
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then
a(n,m) = n!*Sum_{k=0..n} m*C(n-k+m,k)/(n-k+m) * Sum_{j=0..k} C(k,j)/2^k*(2j-k)^(n-k)/(n-k)!.
a(n) ~ n^(n-1) * sqrt((2*s-1)/(s-1)) / (exp(n) * r^(n+1)), where r = 0.6184142504137720756... and s = 2.731257206829781545... are roots of the system of equations r^2*sinh(r*s) = 1, s = 1 + r*cosh(r*s). - Vaclav Kotesovec, Jul 15 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^3/3! + 24*x^4/4! + 65*x^5/5! + 480*x^6/6! +...
PROG
(PARI) {a(n, m=1)=n!*sum(k=0, n, m*binomial(n-k+m, k)/(n-k+m)*sum(j=0, k, binomial(k, j)/2^k*(2*j-k)^(n-k)/(n-k)!))}
CROSSREFS
Cf. A162653.
Sequence in context: A009113 A152751 A369953 * A092468 A347108 A027158
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 09 2009
STATUS
approved