A159996 Numerator of Hermite(n, 17/24).

1, 17, 1, -9775, -167039, 8421137, 383695489, -8028901423, -910021430015, 3028224568337, 2410255364260609, 32253054435619793, -7087387068572072831, -231952136295227242735, 22591990867714977552769, 1319294858293510861104593, -75169387957539018389183999

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..428

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 12^n * Hermite(n, 17/24).

E.g.f.: exp(17*x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 17/12, 1/144, -9775/1728, -167039/20736, ...

Mathematica

Numerator[Table[HermiteH[n, 17/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(17*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A001021 (denominators).

Sequence in context: A139804 A321259 A352073 * A368394 A040284 A040283

Adjacent sequences: A159993 A159994 A159995 * A159997 A159998 A159999

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved