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A160074 Numerator of Hermite(n, 11/26). 1

%I #11 Sep 08 2022 08:45:44

%S 1,11,-217,-9823,111985,14512531,-29616809,-29757197767,-257255805343,

%T 77633648903195,1636542297788551,-244399768017125039,

%U -8773061711366208047,894781780252430869667,48391432742519857724855,-3701801623986784440290839,-286064381868430307508214079

%N Numerator of Hermite(n, 11/26).

%H G. C. Greubel, <a href="/A160074/b160074.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 13^n * Hermite(n, 11/26).

%F E.g.f.: exp(11*x - 169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 11/13, -217/169, -9823/2197, 111985/28561

%t Table[13^n*HermiteH[n, 11/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/26)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A001022 (denominators).

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009

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Last modified April 23 03:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)