A160311 Numerator of Hermite(n, 13/31).

1, 26, -1246, -132340, 3743596, 1114763416, -6992108744, -13037246540656, -244896579015280, 194093391754729376, 9282649209429277216, -3489126110080737399104, -286971048447852951277376, 73011957343257950639722880, 9068569507442760557249311616

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..368

Formula

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 13/31).

a(n+2) = 26*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(26*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 26/31, -1246/961, -132340/29791, 3743596/923521, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 13/31]] (* Harvey P. Dale, Jan 10 2015 *)
Table[31^n*HermiteH[n, 13/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Crossrefs

Cf. A009975 (denominators).

Sequence in context: A091429 A200721 A187463 * A220955 A106710 A114052

Adjacent sequences: A160308 A160309 A160310 * A160312 A160313 A160314

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved