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 A160263 Numerator of Hermite(n, 14/29). 1
 1, 28, -898, -119336, 1189900, 836209808, 13406815624, -8063638544864, -383633726413168, 97762575920121280, 8544799476205933024, -1405112141642673804928, -197439019874757039348032, 22832490910422530976921856, 4956511354073268289737879680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..372 FORMULA From G. C. Greubel, Sep 26 2018: (Start) a(n) = 29^n * Hermite(n, 14/29). E.g.f.: exp(28*x - 841*x^2). a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/29)^(n-2*k)/(k!*(n-2*k)!)). (End) EXAMPLE Numerators of 1, 28/29, -898/841, -119336/24389, 1189900/707281, ... MAPLE seq(coeff(series(factorial(n)*exp(28*x-841*x^2), x, n+1), x, n), n = 0..15); # Muniru A Asiru, Sep 28 2018 MATHEMATICA Table[29^n*HermiteH[n, 14/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *) PROG (PARI) a(n)=numerator(polhermite(n, 14/29)) \\ Charles R Greathouse IV, Jan 29 2016 (PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018 CROSSREFS Cf. A009973 (denominators). Sequence in context: A278195 A095656 A057412 * A129461 A239336 A203135 Adjacent sequences: A160260 A160261 A160262 * A160264 A160265 A160266 KEYWORD sign,frac AUTHOR N. J. A. Sloane, Nov 12 2009 STATUS approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)