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

1, 11, -217, -9823, 111985, 14512531, -29616809, -29757197767, -257255805343, 77633648903195, 1636542297788551, -244399768017125039, -8773061711366208047, 894781780252430869667, 48391432742519857724855, -3701801623986784440290839, -286064381868430307508214079

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, 11/26).

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

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

Example

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

Mathematica

Table[13^n*HermiteH[n, 11/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(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

Crossrefs

Cf. A001022 (denominators).

Sequence in context: A187650 A357083 A214687 * A298889 A204236 A035012

Adjacent sequences: A160071 A160072 A160073 * A160075 A160076 A160077

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved