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A160304
Numerator of Hermite(n, 6/31).
1
1, 12, -1778, -67464, 9442380, 631971792, -83157610296, -8285790028896, 1019373008575632, 139634783587212480, -15957496899294732576, -2875270503337760656512, 302870153404836108243648, 69949680729840145080716544, -6728117484215153259607190400
OFFSET
0,2
LINKS
FORMULA
a(n+2) = 12*a(n+1) - 1922*(n+1)*a(n). - Bruno Berselli, Mar 28 2018
From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 6/31).
E.g.f.: exp(12*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 12/31, -1778/961, -67464/29791, 9442380/923521, ...
MATHEMATICA
Table[31^n*HermiteH[n, 6/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 6/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 6/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
CROSSREFS
Cf. A009975 (denominators).
Sequence in context: A015485 A174775 A145186 * A013479 A090914 A049406
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved