A160192 Numerator of Hermite(n, 3/28).

1, 3, -383, -3501, 439905, 6809283, -841785951, -18540791469, 2254238275137, 64906636872195, -7758232724066751, -277708714711204653, 32620373362042216353, 1404202914087633336771, -162020813910704234524575, -8192328034245044455772973, 928105401692205765637182081

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..417

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 14^n * Hermite(n, 3/28).

E.g.f.: exp(3*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 3/14, -383/196, -3501/2744, 439905/38416, ...

Mathematica

Table[14^n*HermiteH[n, 3/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Crossrefs

Cf. A001023 (denominators)

Sequence in context: A370448 A157577 A062604 * A304424 A316279 A305958

Adjacent sequences: A160189 A160190 A160191 * A160193 A160194 A160195

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved