|
Search: id:A006228
|
|
|
| A006228 |
|
Expansion of exp(arcsin x).
(Formerly M1523)
|
|
+0
10
|
|
| 1, 1, 1, 2, 5, 20, 85, 520, 3145, 26000, 204425, 2132000, 20646925, 260104000, 2993804125, 44217680000, 589779412625, 9993195680000, 151573309044625, 2898026747200000, 49261325439503125, 1049085682486400000
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
REFERENCES
|
L. B. W. Jolley, Summation of Series. 2nd ed., Dover, NY, 1961, p. 150.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..100
|
|
FORMULA
|
i even: a_i = prod_{j=1}^{i/2-1} 1 + 4j^2, i odd: a_i = prod_{j=1}^{(i-1)/2} 2 + 4j(j-1) - Cris Moore (moore(AT)santafe.edu), Jan 31 2001
a(0)=1, a(1)=1, a(n)=(1+(n-2)^2)*a(n-2) for n>=2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 24 2009]
|
|
MATHEMATICA
|
Distribute[ CoefficientList[ Series[ E^ArcSin[x], {x, 0, 21}], x] * Table[ n!, {n, 0, 21}]] (from Robert G. Wilson v Feb 10 2004)
|
|
CROSSREFS
|
Bisections are expansions of sin(asinh(x)) and cos(asinh(x)).
Bisections are A101927 and A101928.
Cf. A002019.
Cf. A166741, A166748. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 24 2009]
Sequence in context: A009737 A008983 A012768 this_sequence A002484 A003069 A115082
Adjacent sequences: A006225 A006226 A006227 this_sequence A006229 A006230 A006231
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
|
|
EXTENSIONS
|
More terms from Christian G. Bower (bowerc(AT)usa.net)
|
|
|
Search completed in 0.002 seconds
|
