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A338632 G.f. A(x) satisfies: 1 = A(x) - x/(A(x) - 3*x/(A(x) - 5*x/(A(x) - 7*x/(A(x) - 9*x/(A(x) - ...))))), a continued fraction relation. 2
1, 1, 2, 14, 166, 2714, 55866, 1377942, 39493518, 1288115570, 47086272754, 1906554619166, 84711219819062, 4098314765667082, 214489189682087594, 12075596389435432230, 727783484288200558110, 46755528594469120151010, 3189788089674119448202722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..200

FORMULA

a(n) = 2 (mod 4) for n > 1 (conjecture).

For n > 0, a(n) = 1 (mod 3) iff n = A191107(k) for some k >= 1 (conjecture).

For n > 0, a(n) = 2 (mod 3) iff n = A186776(k) for some k >= 2 where A186776 is the Stanley sequence S(0,2) (conjecture).

a(n) ~ 2^(2*n) * n^(n - 1/2) / (sqrt(Pi) * exp(n + 1/2)). - Vaclav Kotesovec, Nov 12 2020

EXAMPLE

G.f. A(x) = 1 + x + 2*x^2 + 14*x^3 + 166*x^4 + 2714*x^5 + 55866*x^6 + 1377942*x^7 + 39493518*x^8 + 1288115570*x^9 + 47086272754*x^10 + ...

where

1 = A(x) - x/(A(x) - 3*x/(A(x) - 5*x/(A(x) - 7*x/(A(x) - 9*x/(A(x) - 11*x/(A(x) - 13*x/(A(x) - 15*x/(A(x) - 17*x/(A(x) - 19*x/(A(x) - ...)))))))))), a continued fraction relation.

PROG

(PARI) {a(n) = my(A=[1], CF=1); for(i=1, n, A=concat(A, 0); for(i=1, #A, CF = Ser(A) - (2*(#A-i)+1)*x/CF ); A[#A] = -polcoeff(CF, #A-1) ); A[n+1] }

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

CROSSREFS

Cf. A000699, A158119, A338636.

Cf. A191107, A186776.

Sequence in context: A277362 A209937 A245896 * A124215 A003582 A277373

Adjacent sequences:  A338629 A338630 A338631 * A338633 A338634 A338635

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 04 2020

STATUS

approved

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Last modified June 16 14:36 EDT 2021. Contains 345057 sequences. (Running on oeis4.)