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A160280
Numerator of Hermite(n, 18/29).
1
1, 36, -386, -135000, -2912244, 803439216, 53415783816, -6185340350496, -851589691267440, 52572710870646336, 14783982337749774816, -352049632685279478144, -286207027989716394858816, -3197683221510109228058880, 6143086278048774757772750976
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 18/29).
E.g.f.: exp(36*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 36/29, -386/841, -135000/24389, -2912244/707281, ...
MATHEMATICA
Table[29^n*HermiteH[n, 18/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 18/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
CROSSREFS
Cf. A009973 (denominators).
Sequence in context: A250805 A254644 A034686 * A307959 A095682 A083811
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved