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A224270 Absolute values of the numerators of the third column of ( 0 followed by (mix 0 , A001803(n))/A060818(n) ) and its successive differences. 2
1, 1, 5, 11, 95, 203, 861, 1815, 30459, 63635, 264979, 550069, 4555915, 9412543, 38816525, 79898895, 2627302995, 5392044675, 22104436695, 45256266825, 370241638305, 756514878405, 3088866211275, 6300861570705, 102746354288175, 209286947903319 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The array is

0,          0,      1,     0,   3/2,     0,  15/8, 0,...

0,          1,     -1,   3/2,  -3/2,  15/8, -15/8,...

1,         -2,    5/2,    -3,  27/8, -15/4,...

-3,       9/2,  -11/2,  51/8, -57/8,...

15/2,     -10,   95/8, -27/2,...

-35/2,  175/8, -203/8,...

315/8, -189/4,...

-693/8,...

Note A001803 in the first column and a variant of A206771(n) in the second column.

Now consider a(n)/A046161(n) and its differences:

1,            1/2,     5/8,  11/16,  95/128, 203/256, 861/1024,...

-1/2,         1/8,    1/16,  7/128,  13/256, 49/1024,...   =b(n)/A046161(n)

5/8,        -1/16,  -1/128, -1/256, -3/1024,...

-11/16,     7/128,   1/256, 1/1024,...

95/128,   -13/256, -3/1024,...

-203/256, 49/1024,...

861/1024,...

This an autosequence of second kind. The first column is the signed sequence.

(Its companion, the corresponding autosequence of first kind, is 0, 1, 1, 9/8, 5/4,... in A206771).

Main diagonal: 1, 1/8, -1/128,... = A002596(n)/A061549(n) ?

b(n) = a(n+1) - A171977*a(n). Also for two successive rows (with shifted A171977).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Numerators of (0, 0 followed by A001803(n)/(4*A046161(n))) + A001790(n)/A046161(n).

EXAMPLE

a(n)=numerators of 0+1=1, 0+1/2=1/2, 1/4+3/8=5/8, 3/8+5/16=11/16, 15/32+35/128=95/128,... .

MATHEMATICA

nmax = 25; t1 = Table[ Numerator[ (2*n+1)*(Binomial[2*n, n]/4^n)] / Denominator[ Binomial[2*n, n]/4^n], {n, 0, Ceiling[nmax/2]}]; t2 = Join[{0}, Table[ If[ OddQ[n], 0, t1[[n/2]] ], {n, 1, nmax+2}] ]; t3 = Table[ Differences[t2, n], {n, 0, nmax}]; t3[[All, 3]] // Numerator // Abs (* Jean-François Alcover, Apr 02 2013 *)

CROSSREFS

Cf. A098597

Sequence in context: A353890 A120778 A042761 * A123025 A053778 A030079

Adjacent sequences:  A224267 A224268 A224269 * A224271 A224272 A224273

KEYWORD

nonn,frac,tabl,less

AUTHOR

Paul Curtz, Apr 02 2013

EXTENSIONS

More terms from Jean-François Alcover, Apr 02 2013

STATUS

approved

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Last modified October 5 20:00 EDT 2022. Contains 357261 sequences. (Running on oeis4.)