login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A159869
Numerator of Hermite(n, 5/23).
1
1, 10, -958, -30740, 2733292, 157424600, -12884868680, -1128180047600, 84143536968080, 10390351292567200, -697311246084385760, -116903029136204833600, 6946277990568033138880, 1553663637818936898774400, -80002471104083358804411520, -23812890514414926932690528000
OFFSET
0,2
LINKS
FORMULA
a(n) = 10*a(n-1) + 1058*(1-n)*a(n-2). - Robert Israel, Dec 07 2017
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 23^n * Hermite(n, 5/23).
E.g.f.: exp(10*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 10/23, -958/529, -30740/12167, 2733292/279841
MAPLE
f:= gfun:-rectoproc({a(n) = -(1058*n-1058)*a(n-2)+10*a(n-1), a(0) = 1, a(1) = 10}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Dec 07 2017
MATHEMATICA
Numerator[Table[HermiteH[n, 5/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 5/23], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 5/23)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018
CROSSREFS
Cf. A009967 (denominators)
Sequence in context: A015008 A194791 A292669 * A006242 A163566 A168520
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved