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A238800 Unreduced numerators in triangle that leads to the Euler numbers A198631(n)/A006519(n+1). 1
1, 1, 1, -2, 1, -3, 1, -4, 2, 1, -5, 5, 1, -6, 9, -10, 1, -7, 14, -35, 1, -8, 20, -80, 26, 1, -9, 27, -150, 117, 1, -10, 35, -250, 325, -454, 1, -11, 44, -385, 715, -2497, 1, -12, 54, -560, 1365, -8172, 5914, 1, -13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

We use the array ASPEC mentioned in A191302:

2, 1,  1,  1,  1,  1,   1,   1,...

2, 3,  4,  5,  6,  7,   8,   9,...

2, 5,  9, 14, 20, 27,  35,  44,...

2, 7, 16, 30, 50, 77, 112, 156,...

with the first upper diagonal of the difference table of the autosequence A198631(n)/A006519(n+1), i.e., 1/2, -1/4, 1/4, -5/8, 13/4, -227/8, 2957/8,...

written by columns:

1/2

1/2,

1/2, -1/4,

1/2, -1/4,

1/2, -1/4, 1/4,

1/2, -1/4, 1/4,

1/2, -1/4, 1/4, -5/8,

1/2, -1/4, 1/4, -5/8,

etc.

Hence, by multiplication of this double triangle by ASPEC, the beginning of the double triangle ESPEC is obtained:

E(0) =     1 =   1

E(1) =   1/2 = 1/2

E(2) =     0 = 1/2 -2/4

E(3) =  -1/4 = 1/2 -3/4

E(4) =     0 = 1/2 -4/4  +2/4

E(5) =   1/2 = 1/2 -5/4  +5/4

E(6) =     0 = 1/2 -6/4  +9/4 -10/8

E(7) = -17/8 = 1/2 -7/4 +14/4 -35/8

E(8) =     0 = 1/2 -8/4 +20/4 -80/8 +26/4.

The terms of the sequence are the reduced numerators. Like A192456(n) for Bernoulli numbers A164555(n)/A027642(n).

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

a(n) by triangle

1,

1,

1, -2,

1, -3,

1, -4,  2,

1, -5,  5,

1, -6,  9, -10,

1, -7, 14, -35,

1, -8, 20, -80, 26,

etc.

CROSSREFS

Sequence in context: A216477 A195836 A132460 * A067734 A303758 A161904

Adjacent sequences:  A238797 A238798 A238799 * A238801 A238802 A238803

KEYWORD

sign,tabf

AUTHOR

Paul Curtz, Mar 05 2014

STATUS

approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)