|
EXAMPLE
|
E.g.f.: A(x) = 1 + x + 4*x^2/2! + 31*x^3/3! + 368*x^4/4! + 5941*x^5/5! +...
Related expansions.
A(x)^2 = 1 + 2*x + 10*x^2/2! + 86*x^3/3! + 1080*x^4/4! + 18042*x^5/5! +...
1/(1 + sinh(x))^2 = 1 - 2*x + 6*x^2/2! - 26*x^3/3! + 144*x^4/4! - 962*x^5/5! +...
Coefficients of [x^n/n!] in the odd powers of (1 + sinh(x)) begin:
1: [(1), 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,...];
3: [1,(3), 6, 9, 24, 63, 96, 549, 384, 4923, 1536, 44289,...];
5: [1, 5,(20), 65, 200, 725, 2720, 9665, 41600, 165125,...];
7: [1, 7, 42,(217), 1008, 4627, 22512, 112357, 567168,...];
9: [1, 9, 72, 513,(3312), 20169, 122112, 756513, 4770432,...];
11:[1, 11, 110, 1001, 8360,(65351), 492800, 3693701, 27948800,...];
13:[1, 13, 156, 1729, 17784, 171613,(1581216), 14210209,...];
15:[1, 15, 210, 2745, 33600, 387675, 4262160,(45293445),...];
17:[1, 17, 272, 4097, 58208, 783377, 10057472, 124378817,(1498389248), ...]; ...
where the coefficients in parenthesis generate this sequence like so:
[1, 3/3, 20/5, 217/7, 3312/9, 65351/11, 1581216/13, 45293445/15,...].
|