The On-Line Encyclopedia of Integer Sequences (OEIS)

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A158958

Numerator of Hermite(n, 3/4).
(history; published version)

#25 by Charles R Greathouse IV at Thu Sep 08 08:45:43 EDT 2022

PROG

(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(3/2)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#24 by Michel Marcus at Sat Feb 06 07:42:26 EST 2021

STATUS

reviewed

approved

#23 by Joerg Arndt at Sat Feb 06 07:42:10 EST 2021

STATUS

proposed

reviewed

#22 by R. J. Mathar at Sat Feb 06 07:25:37 EST 2021

STATUS

editing

proposed

#21 by R. J. Mathar at Sat Feb 06 07:24:19 EST 2021

LINKS

DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)

FORMULA

Conjecture: D-finite with recurrence a(n) - 3*a(n-1) + 8*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

STATUS

approved

editing

#20 by Bruno Berselli at Wed Jul 11 04:34:30 EDT 2018

STATUS

reviewed

approved

#19 by Michel Marcus at Wed Jul 11 01:09:23 EDT 2018

STATUS

proposed

reviewed

#18 by Jon E. Schoenfield at Wed Jul 11 00:26:06 EDT 2018

STATUS

editing

proposed

#17 by Jon E. Schoenfield at Wed Jul 11 00:26:03 EDT 2018

CROSSREFS

Cf. A000079 (denominators).

#16 by Jon E. Schoenfield at Wed Jul 11 00:25:55 EDT 2018

FORMULA

Conjecture: a(n) - 3*a(n-1) + 8*(n-1)*a(n-2) = 0. - R. J. Mathar, Feb 16 2014

EXAMPLE

Numerator of 1, 3/2, 1/4, -45/8, -159/16, 963/32, 9249/64, -18477/128, -573375/256, ...

MATHEMATICA

Numerator[Table[HermiteH[n, 3/4], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)

STATUS

proposed

editing