A103366 Second column of triangle A103364, which equals the matrix inverse of the Narayana triangle (A001263).
1, -3, 12, -70, 585, -6741, 103068, -2023092, 49615695, -1487006785, 53477384268, -2272859942574, 112699083156751, -6447858833644515, 421601806346674320, -31242589674606301224, 2604618355967848204587, -242686626407684239621113, 25124942798118355122058980
Offset: 2
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 2..200
Programs
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PARI
a(n)=if(n<2,0,(matrix(n,n,m,j,binomial(m-1,j-1)*binomial(m,j-1)/j)^-1)[n,2])
Formula
a(n) ~ (-1)^n * 2^(2*n-5) * n! * (n-1)! / (BesselJ(2, BesselJZero(1, 1)) * BesselJZero(1, 1)^(2*n-4)), where BesselJZero(1, 1) = A115369. - Vaclav Kotesovec, Jul 11 2025