A160072 Numerator of Hermite(n, 7/26).

1, 7, -289, -6755, 245761, 10853087, -339364481, -24385611803, 632237079425, 70364353871287, -1430714718511841, -247846519114532947, 3584471689625294209, 1030356783355922692495, -8537671120722083906881, -4935411996685280768234507, 8738108605264000030245121

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..422

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 13^n * Hermite(n, 7/26).

E.g.f.: exp(7*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 7/13, -289/169, -6755/2197, 245761/28561

Mathematica

Table[13^n*HermiteH[n, 7/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/13)^(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

Crossrefs

Cf. A001022 (denominators).

Sequence in context: A209889 A176072 A096548 * A137435 A220241 A041851

Adjacent sequences: A160069 A160070 A160071 * A160073 A160074 A160075

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved