|
EXAMPLE
|
E.g.f.: A(x) = 1 + x + 4*x^2/2! + 31*x^3/3! + 360*x^4/4! + 5601*x^5/5! +...
The coefficients in initial powers of G(x) = 1/(1 - sinh(x)) begin:
G^1: [(1), 1, 2, 7, 32, 181, 1232, 9787, 88832, ..., A006154(n), ...];
G^2: [1,(2), 6, 26, 144, 962, 7536, 67706, ...];
G^3: [1, 3,(12), 63, 408, 3123, 27552, 275103, ...];
G^4: [1, 4, 20,(124), 920, 7924, 77600, 850924, ...];
G^5: [1, 5, 30, 215,(1800), 17225, 185280, 2211515, ...];
G^6: [1, 6, 42, 342, 3192,(33606), 393792, 5080662, ...];
G^7: [1, 7, 56, 511, 5264, 60487, (766976), 10634911, ...];
G^8: [1, 8, 72, 728, 8208, 102248, 1395072,(20689208), ...]; ...
where coefficients in parenthesis form initial terms of this sequence:
[1/1, 2/2, 12/3, 124/4, 1800/5, 33606/6, 766976/7, 20689208/8, ...].
|