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A219976 Denominators of the Inverse bi-binomial transform of A164558(n)/A027642(n) read downwards antidiagonals. 0
1, 2, 2, 6, 6, 6, 1, 3, 3, 1, 30, 30, 30, 30, 30, 1, 15, 15, 15, 15, 1, 42, 42, 210, 210, 210, 42, 42, 1, 21, 21, 105, 105, 21, 21, 1, 30, 30, 210, 210, 210, 210, 210, 30, 30, 1, 15, 15, 105, 105, 105, 105, 15, 15, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Starting from any sequence a(k) in the first row, we define the array T(n,k) of the inverse bi-binomial transform by T(0,k) = a(k), T(n,k) = T(n-1,k+1) -2*T(n-1,k) n>0. Hence A164558(n)/A027642(n) and successive "bi-differences":

1,       3/2,    13/6,       3,  119/30,        5,   253/42,       7,  239/30, 9;

-1/2,   -5/6,    -4/3,  -61/30,  -44/15,  -167/42,  -106/21, -181/30, -104/15;

1/6,     1/3,   19/30,   17/15, 397/210,    61/21 , 853/210,   77/15;

0,     -1/30,   -2/15, -79/210, -92/105, -367/210, -314/105;

-1/30, -1/15, -23/210, -13/105,   1/210,   53/105;

0,      1/42,    2/21,  53/210,  52/105;

1/42,   1/21,  13/210,  -1/105;

0,     -1/30,   -2/15;

-1/30, -1/15;

0.

The first column is A027641(n)/A027642(n).

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

Partial array of denominators:

1,   2,   6,   1,  30,   1,  42,  1, 30,  1;

2,   6,   3,  30,  15,  42,  21, 30, 15;

6,   3,  30,  15, 210,  21, 210, 15;

1,  30,  15, 210, 105, 210, 105;

30, 15, 210, 105, 210, 105;

1,  42,  21, 210, 105;

42, 21, 210, 105;

1,  30,  15;

30, 15;

1.

a(n):

1;

2,   2;

6,   6,  6,;

1,   3,  3,  1;

30, 30, 30, 30, 30;

MATHEMATICA

A164558[n_] := Sum[(-1)^k*Binomial[n, k]*BernoulliB[k], {k, 0, n}] // Numerator; t[0, k_?Positive] := A164558[k] / Denominator[ BernoulliB[k]]; t[n_?Positive, k_] := t[n, k] = t[n-1, k+1] - 2*t[n-1, k]; t[0, 0] = 1; t[_, _] = 0; Flatten[ Table[t[n-k , k] // Denominator, {n, 0, 9}, {k, 0, n}]] (* Jean-François Alcover, Dec 04 2012 *)

CROSSREFS

Cf. A213268.

Sequence in context: A247377 A167909 A185421 * A063944 A086447 A324032

Adjacent sequences:  A219973 A219974 A219975 * A219977 A219978 A219979

KEYWORD

nonn,tabl,less

AUTHOR

Paul Curtz, Dec 02 2012

STATUS

approved

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Last modified June 28 00:25 EDT 2022. Contains 354903 sequences. (Running on oeis4.)