[seqfan] Definition of A002190
Paul D Hanna
pauldhanna at juno.com
Sat Oct 9 23:52:01 CEST 2010
Seqfans,
The definition of A002190 is:
Sum_{n>=0} a(n)*x^n/n!^2 = -ln(BesselJ(0,2*sqrt(x))).
[1, 4, 33, 456, 9460, 274800, 10643745, 530052880, 32995478376, 2510382661920, ...]
(OFFSET 2).
However, by the definition the offset should be 1 and a(1) = 1, since
-log( Sum_{n>=0} (-x)^n/n!^2 ) = x + x^2/2!^2 + 4*x^3/3!^2 + 33*x^4/4!^2 + 456*x^5/5!^2 + 9460*x^6/6!^2 +...
The question is, should the sequence be changed to include a(1)=1,
or should the definition be changed to fit the existing sequence, i.e.,
change the name to:
Sum_{n>=0} a(n)*x^n/n!^2 = -x-ln(BesselJ(0,2*sqrt(x))).
I would vote for prepending a '1' to the existing sequence and changing OFFSET=1 to fit the definition,
but I fear changing an old classic sequence without the consensus of SeqFans.
Thanks,
Paul
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