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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 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 January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)