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A160396
Numerator of Hermite(n, 13/32).
0
1, 13, -343, -17771, 295825, 40240733, -234182471, -126663903899, -807320774623, 508320180300205, 10328296473365449, -2468331468983298763, -90257274834777092687, 13992083972581285394941, 782649512943833039058905, -90120814247192824203171323
OFFSET
0,2
FORMULA
Empirical e.g.f.: exp(13*x-256*x^2). - Simon Plouffe, Jun 20 2018
a(n) = 32^n*KummerU(-n/2, 1/2, (13/32)^2). - Peter Luschny, Jun 20 2018
D-finite with recurrence a(n) -13*a(n-1) +512*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021
EXAMPLE
Numerators of 1, 13/16, -343/256, -17771/4096, 295825/65536,...
MAPLE
a := n -> 32^n*KummerU(-n/2, 1/2, (13/32)^2):
seq(simplify(a(n)), n=0..15); # Peter Luschny, Jun 20 2018
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 13/32]] (* Harvey P. Dale, Oct 03 2011 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 13/32)) \\ Charles R Greathouse IV, Jan 29 2016
CROSSREFS
Cf. A001025 (denominators).
Sequence in context: A096717 A296679 A125119 * A253125 A297070 A220636
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved