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A160290
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Numerator of Hermite(n, 28/29).
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1
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1, 56, 1454, -106960, -13326644, -26665184, 110583825736, 6461799278144, -940153204639600, -139598550546523264, 6414520381228962016, 2707260761541343173376, 32925146552816962489024, -52799543003992720712035840, -3676715662747488061659005824
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..372
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FORMULA
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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)
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EXAMPLE
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Numerators of 1, 56/29, 1454/841, -106960/24389, -13326644/707281, ...
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MATHEMATICA
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Table[29^n*HermiteH[n, 28/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
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PROG
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(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
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CROSSREFS
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Cf. A009973 (denominators).
Sequence in context: A278079 A025597 A034202 * A030649 A319310 A022081
Adjacent sequences: A160287 A160288 A160289 * A160291 A160292 A160293
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, Nov 12 2009
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STATUS
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approved
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