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A159967 Numerator of Hermite(n, 7/24). 1
1, 7, -239, -5705, 166561, 7738087, -185681231, -14671182953, 271635081025, 35703851090887, -454151172380591, -106006149348418697, 696707868662781409, 371234207228774486695, -9834809672032188431, -1496885167214122955673257, -10435709792715681635690879 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 12^n * Hermite(n, 7/24).
E.g.f.: exp(7*x - 144*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/12)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 7/12, -239/144, -5705/1728, 166561/20736, ...
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 7/24]] (* Harvey P. Dale, Jan 27 2012 *)
Table[12^n*HermiteH[n, 7/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 7/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
CROSSREFS
Cf. A001021 (denominators).
Sequence in context: A120661 A366703 A185389 * A349046 A139057 A251594
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified May 22 10:24 EDT 2024. Contains 372745 sequences. (Running on oeis4.)