|
| |
|
|
A136727
|
|
E.g.f.: A(x) = [ exp(x)/(3 - 2*exp(x)) ]^(1/3).
|
|
4
| |
|
|
1, 1, 3, 17, 139, 1481, 19443, 303297, 5480219, 112549881, 2589274883, 65957355377, 1842897053099, 56038776055081, 1842278768795923, 65109900167188257, 2461735422517374779, 99148196540813749081
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| G.f. of variant A014307 is B(x) = sqrt(exp(x)/(2-exp(x))), which satisfies: B(x) = 1 + integral(B(x)^3*exp(-x)).
|
|
|
FORMULA
| E.g.f. A(x) satisfies: A(x) = 1 + integral( A(x)^4 * exp(-x) ).
O.g.f.: 1/(1 - x/(1-2*x/(1 - 4*x/(1-4*x/(1 - 7*x/(1-6*x/(1 - 10*x/(1-8*x/(1 - 13*x/(1-10*x/(1 - ...)))))))))), a continued fraction.
|
|
|
EXAMPLE
| E.g.f.: A(x) = 1 + x + 3/2*x^2 + 17/6*x^3 + 139/24*x^4 + 1481/120*x^5 +...
|
|
|
PROG
| (PARI) {a(n)=n!*polcoeff((exp(x +x*O(x^n))/(3-2*exp(x +x*O(x^n))))^(1/3), n)} (PARI) /* As solution to integral equation: */ {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+intformal(A^4*exp(-x+x*O(x^n)))); n!*polcoeff(A, n)} for(n=0, 41, print1(a(n), ", "))
|
|
|
CROSSREFS
| Cf. A201339, variants: A014307, A136728, A136729.
Sequence in context: A006290 A060003 A025167 * A062873 A120022 A001865
Adjacent sequences: A136724 A136725 A136726 * A136728 A136729 A136730
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
|
| |
|
|
