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A160290 Numerator of Hermite(n, 28/29). 1
1, 56, 1454, -106960, -13326644, -26665184, 110583825736, 6461799278144, -940153204639600, -139598550546523264, 6414520381228962016, 2707260761541343173376, 32925146552816962489024, -52799543003992720712035840, -3676715662747488061659005824 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 28/29).
E.g.f.: exp(56*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(56/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 56/29, 1454/841, -106960/24389, -13326644/707281, ...
MATHEMATICA
Table[29^n*HermiteH[n, 28/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 28/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(56*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(56/29)^(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: A278079 A025597 A034202 * A030649 A319310 A022081
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)