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A216966 O.g.f.: 1/(1 - x/(1 - 2^3*x/(1 - 3^3*x/(1 - 4^3*x/(1 - 5^3*x/(1 - 6^3*x/(1 -...))))))), a continued fraction. 3
1, 1, 9, 297, 24273, 3976209, 1145032281, 530050022073, 369626762653857, 369614778179835681, 509880429246329788329, 940535818601273787325257, 2261104378216803649437779313, 6933711495845384616312688513329, 26630255658298074277771723491847161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the continued fraction o.g.f. for the Euler numbers (A000364):

1/(1-x/(1-2^2*x/(1-3^2*x/(1-4^2*x/(1-5^2*x/(1-6^2*x/(1-...))))))).

LINKS

Table of n, a(n) for n=0..14.

FORMULA

G.f.: T(0), where T(k) = 1 - x*(k+1)^3/(x*(k+1)^3 -1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 12 2013

a(n) ~ c * d^n * (n!)^3 / sqrt(n), where d = 1.450930901627203932388423902788627... and c = 0.8323271443586650769764930497... - Vaclav Kotesovec, Aug 25 2017

EXAMPLE

G.f.: A(x) = 1 + x + 9*x^2 + 297*x^3 + 24273*x^4 + 3976209*x^5 +...

MATHEMATICA

nmax = 20; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]^3*x]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 25 2017 *)

PROG

(PARI) {a(n)=local(CF=1+x*O(x^n)); for(k=1, n, CF=1/(1-(n-k+1)^3*x*CF)); polcoeff(CF, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A000364, A227887.

Sequence in context: A129934 A003303 A012838 * A211077 A211082 A061685

Adjacent sequences:  A216963 A216964 A216965 * A216967 A216968 A216969

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 20 2012

STATUS

approved

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Last modified February 20 07:28 EST 2020. Contains 332067 sequences. (Running on oeis4.)