A240776 Define a square array B(m,n) (m>=0, n>=0) by B(n, n) = A212196(n)/A181131(n), B(n, n+1) = -A212196(n)/A181131(n), B(m, n) = B(m, n-1) + B(m+1, n-1); a(n) = numerator of B(0,n).

1, -1, -4, -1, -8, -1, -8, -3, -8, 1, 104, -41, -920, 1767, 20168, -8317, -2022392, 869807, 291391192, -129169263, -2759924456, 250158593, 146772324808, -67632514765, -10164962436952

Offset

0,3

Comments

The array B(m,n) begins:

1, -1, -4/3, -1, -8/15, -1/5, -8/105,...

-2, -1/3, 1/3, 7/15, 1/3, 13/105,...

5/3, 2/3, 2/15, -2/15, -22/105,...

-1, -8/15, -4/15, -8/105,...

7/15, 4/15, 4/21,...

-1/5, -8/105,...

13/105,...

etc.

B(0, n) = 1, -1, -4/3, -1, -8/15, -1/5, -8/105, -3/35, -8/105, 1/35, 104/1155, ... = a(n)/b(n).

The main diagonal is A212196(n)/A181131(n).

The first upper diagonal is -A212196(n)/A181131(n).

Links

Table of n, a(n) for n=0..24.

Mathematica

max = 12; t[0] = Table[BernoulliB[n], {n, 0, 2*max}]; t[n_] := t[n] = Differences[t[0], n]; B1[1, 1] = -1/3; B1[n_, n_] := t[n][[n+1]]; B1[m_, n_] /; n == m+1 := B1[m, n] = -B1[m, m]; B1[m_?NonNegative, n_?NonNegative] := B1[m, n] = B1[m, n-1] + B1[m+1, n-1]; B1[_, _] = 0; Table[B1[0, n] // Numerator, {n, 0, 2*max}] (* Jean-François Alcover, Apr 14 2014 *)

Crossrefs

Sequence in context: A179836 A334451 A040019 * A019768 A319296 A211779

Adjacent sequences: A240773 A240774 A240775 * A240777 A240778 A240779

Keyword

sign,frac

Author

Paul Curtz, Apr 12 2014

Extensions

More terms from Jean-François Alcover, Apr 14 2014

Edited by N. J. A. Sloane, May 21 2014

Status

approved