A159507 Numerator of Hermite(n, 1/14).
1, 1, -97, -293, 28225, 143081, -13687169, -97818797, 9291579137, 85981515985, -8109191282849, -92371076948149, 8649337125963073, 117277723616986297, -10901977774859968705, -171807014577365168189, 15854100314466788828161, 285247499171775372548513
Offset: 0
Examples
G.f. = 1 + x - 97*x^2 - 293*x^3 + 28225*x^4 + 143081*x^5 - 13687169*x^6 + ...
Links
- T. D. Noe, Table of n, a(n) for n = 0..100
Programs
-
Magma
[Numerator((&+[(-1)^k*Factorial(n)*(1/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
-
Mathematica
Numerator[Table[HermiteH[n, 1/14], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *) a[ n_] := If[ n < 0, 0, HermiteH[n, 1/14] 7^n]; (* Michael Somos, Jan 24 2014 *) a[ n_] := Sum[(-49)^k n! / (k! (n - 2 k)!), {k, 0, n/2}]; (* Michael Somos, Jan 24 2014 *) -
PARI
{a(n) = if( n<0, 0, sum(k=0, n\2, (-49)^k * n! / (k! * (n - 2*k)!)))}; \\ Michael Somos, Jan 24 2014
Formula
a(n) = Sum_{k = 0..n/2} (-49)^k * n! / (k! * (n - 2*k)!). - Michael Somos, Jan 24 2014
0 = a(n) * (-98*a(n+1) + a(n+2) - a(n+3)) + a(n+1) * (-a(n+1) + a(n+2)) for all n in Z. - Michael Somos, Jan 24 2014
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 7^n * Hermite(n,1/14).
E.g.f.: exp(x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/7)^(n-2*k)/(k!*(n-2*k)!)). (End)