[seqfan] Re: A000657 Median Euler numbers

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2010-December/006728.html

sai> From seqfan-bounces at list.seqfan.eu Wed Dec 22 21:20:05 2010
sai>: "Sean A. Irvine"
sai>
sai>    [different from value in OEIS, 1731678144472]

Whereas this looks like a typo (who would care for a single 4 in such
a large number :-), I get really different results (ignoring signs)
for sufficiently large n if I remove the "evalf" in A002832's Maple:

rr := array(1..40, 1..40):
rr[1, 1] := 0:
for i from 1 to 39 do
        rr[i+1, 1] := subs(x=0, diff((exp(x)-1)/cosh(x), x$i)):
od:
for i from 2 to 40 do
        for j from 2 to i do
                rr[i, j] := rr[i, j-1]-rr[i-1, j-1]:
        od:
od:
seq(rr[2*i-1, i-1], i=2..20);

output:

1, -3, 24, -402, 11616, -514608, 32394624, -2748340752, 302234850816,
    -41811782731008, 7106160248346624, -1455425220196234752,
    353536812021243273216, -100492698847094242603008,
    33045185784774350171111424, -12446666782183358249311537152,
    5323718659259504892710722338816, -2566197976670748764846449803460608,
    1384674200979566019538447532463489024

Differences sneak in for -2748340752 which is 5 off the value in the sequence,
then 302234850816 is 493 off etc. Any independent opinions on this, say, via
expansion of the g.f.?

Richard Mathar