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A190352 The continued fraction expansion of tanh(Pi) requires the computation of the pairs (p_n, q_n); sequence gives values of q_n. 2
1, 1, 268, 1073, 15290, 16363, 48016, 64379, 176774, 417927, 594701, 1607329, 5416688, 44940833, 140239187, 185180020, 1066139287, 4449737168, 5515876455, 81672007538, 822235951835, 903907959373, 18900395139295, 719118923252583, 738019318391878 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(2) = 268 explains the comment in A021085 that "The decimal expansion of Sum_{n>=1} floor(n * tanh(Pi))/10^n is the same as that of 1/81 for the first 268 decimal places [Borwein et al.]".

REFERENCES

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 13.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1920

FORMULA

a(n) = A060402(n)*a(n-1) + a(n-2) for n >= 2. - Nathaniel Johnston, May 10 2011

MAPLE

lim:=50: with(numtheory): cfr := cfrac(tanh(Pi), lim+10, 'quotients'): q[0]:=1:q[1]:=cfr[2]: printf("%d, %d, ", q[0], q[1]): for n from 2 to lim do q[n]:=cfr[n+1]*q[n-1]+q[n-2]: printf("%d, ", q[n]): od: # Nathaniel Johnston, May 10 2011

MATHEMATICA

a[0] := 1; a[1] := 1; A060402:= ContinuedFraction[Tanh[Pi], 100];

a[n_]:= a[n] = A060402[[n + 1]]*a[n - 1] + a[n - 2]; Join[{1, 1}, Table[a[n], {n, 2, 75}]] (* G. C. Greubel, Apr 05 2018 *)

CROSSREFS

Cf. A060402, A021085.

Sequence in context: A194774 A279184 A237228 * A235175 A235169 A352474

Adjacent sequences:  A190349 A190350 A190351 * A190353 A190354 A190355

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 09 2011

EXTENSIONS

a(4)-a(24) from Nathaniel Johnston, May 10 2011

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)