A381195 Expansion of g.f. (1 - sqrt(1 - 1728*x))/(864*x).
1, 432, 373248, 403107840, 487599243264, 631928619270144, 857978513934778368, 1204601833564428828672, 1734626640332777513287680, 2547819609320783611516944384, 3802273336964543978787469000704, 5749037285490390495926653129064448, 8788066841328079995004188536982208512
Offset: 0
Keywords
Links
- S. Hassani, J.-M. Maillard, and N. Zenine, On the diagonals of rational functions: the minimal number of variables (unabridged version), arXiv:2502.05543 [math-ph], 2025. See p. 23.
Programs
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Mathematica
CoefficientList[Series[(1-Sqrt[1-1728x])/(864x),{x,0,12}],x]
Formula
a(n) = (-27)^n*2^(1+6*n)*binomial(1/2,1+n).
E.g.f.: exp(864*x)*(BesselI(0, 864*x) - BesselI(1, 864*x)).
D-finite with recurrence (n+1)*a(n) +864*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Feb 18 2025
a(n) ~ 1728^n / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, May 29 2025