A159622 Numerator of Hermite(n, 5/19).

1, 10, -622, -20660, 1140652, 71072600, -3407027720, -341956780400, 13799550292880, 2113137866519200, -68538099137942240, -15942236387648046400, 384907219477056806080, 141972608257353242070400, -2193013079438122761162880, -1456989255059707798459232000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..397

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 19^n * Hermite(n, 5/19).

E.g.f.: exp(10*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 5/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 5/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/19)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A159564, A159618.

Sequence in context: A042751 A285372 A308145 * A115692 A179889 A209472

Adjacent sequences: A159619 A159620 A159621 * A159623 A159624 A159625

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved