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A227887 O.g.f.: 1/(1 - x/(1 - 2^4*x/(1 - 3^4*x/(1 - 4^4*x/(1 - 5^4*x/(1 - 6^4*x/(1 -...))))))), a continued fraction. 2
1, 1, 17, 1585, 485729, 372281761, 601378506737, 1820943071778385, 9489456505643743169, 79759396929125826861121, 1027412704023984825792488657, 19464301715272748317827942755185, 524230105465412991467916306841439009, 19509134827116013764271741468197795034081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the continued fraction 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..13.

FORMULA

a(n) ~ c * d^n * (n!)^4 / sqrt(n), where d = 16 / EllipticK[1/2]^4 (Mathematica notation) = 16 / EllipticK(1/sqrt(2))^4 (Maple notation) = 1.353976395034780345656335026823167975194023955584218523125862439033... and c = 0.92842239546346589489931052879575759281033... - Vaclav Kotesovec, Aug 25 2017

Equivalently, d = 4096 * Pi^2 / Gamma(1/4)^8. - Vaclav Kotesovec, Sep 27 2019

EXAMPLE

G.f.: A(x) = 1 + x + 17*x^2 + 1585*x^3 + 485729*x^4 + 372281761*x^5 +...

MATHEMATICA

nmax = 20; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]^4*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)^4*x*CF)); polcoeff(CF, n)}

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

CROSSREFS

Cf. A000364, A216966.

Sequence in context: A104808 A061686 A133590 * A144571 A242228 A222905

Adjacent sequences:  A227884 A227885 A227886 * A227888 A227889 A227890

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 26 2013

STATUS

approved

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Last modified November 18 07:20 EST 2019. Contains 329251 sequences. (Running on oeis4.)