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A160287
Numerator of Hermite(n, 25/29).
1
1, 50, 818, -127300, -10492628, 331843000, 104835151480, 1892798018000, -1139689172625520, -82453948761484000, 13129917257130921760, 2043371281024706968000, -140761165040200966003520, -48281464188212733742288000, 663810425358397635518568320
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 25/29).
E.g.f.: exp(50*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 50/29, 818/841, -127300/24389, -10492628/707281, ...
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 25/29]] (* Harvey P. Dale, Dec 05 2012 *)
Table[29^n*HermiteH[n, 25/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 25/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(50*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(50/29)^(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: A128799 A231835 A206120 * A104672 A086027 A110929
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved