[seqfan] Reproducing A002771 skew determinants

[Sean A. Irvine]

I have been trying to reproduce the terms of A002771 (terms in a skew determinant).

Based on Sylvester (1879), an exponential generating function for the sequence is exp(x+x^2/4) / (1-x^2)^(1/4).

Using the example in Muir (1906-1923), another formula appears to be

a(n) = sum(binomial(n, n - 2*k) * A002370(k), k=0..floor(n/2)).

Both the egf and summation formula produce the following sequence:

1, 2, 4, 13, 41, 226, 1072, 9059, 58123, 657766, 5268836, 73980787, ...

but this disagrees with the OEIS after term 7:

1, 2, 4, 13, 41, 226, 1072, 9374, 60958, 723916, 5892536, 86402812, ...

Page 282 of Muir only lists the sequence up to 1072:

http://quod.lib.umich.edu/cache/a/c/m/acm9350.0003.001/00000301.tif.20.pdf#page=11;zoom=75

So my question is where did the current terms in the OEIS after 1072 come from?  Does anyone have access to Muir (1896) which might be the original source?

I am loathe to change the terms of such as old sequence.  Would the correct course of action be to create a new sequence using above formulas and link the original as a potential erroneous version?

Finally, the Rivera (2014) paper attached to A002771 does not appear to be relevant and I could see no reference to the sequence in that paper.  It does mention, A027771 -- so perhaps it has been attached to the wrong sequence?

Regards,
Sean.