This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159858 #28 Sep 08 2022 08:45:44 %S A159858 1,2,-1054,-6340,3332716,33496312,-17563075016,-247760738608, %T A159858 129576612091280,2356200115760672,-1229116100101646816, %U A159858 -27386829424951203392,14249679514133063237824,376202545407446604740480,-195237686946571258563550336,-5962787476468241626543090432 %N A159858 Numerator of Hermite(n, 1/23). %C A159858 Consider any odd integer k. B(n) = k^n Hermite(n,1/k) satisfies the recurrence B(n) = 2*B(n-1) - 2*k^2*(n-1)*B(n-2) with B(0) = 1 and B(1) = 2. In particular, B(n) == 2*B(n-1) mod k, and B(n) is coprime to k. Therefore B(n) is the numerator of Hermite(n,1/k). - _Robert Israel_, Jun 27 2014 %H A159858 G. C. Greubel, <a href="/A159858/b159858.txt">Table of n, a(n) for n = 0..385</a> %H A159858 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x) %F A159858 D-finite with recurrence a(n) - 2*a(n-1) + 1058*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014 %F A159858 a(n) = 23^n * Hermite(n,1/23). This does satisfy the above formula. - _Robert Israel_, Jun 27 2014 %F A159858 From _G. C. Greubel_, Jun 09 2018: (Start) %F A159858 E.g.f.: exp(2*x-529*x^2). %F A159858 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/23)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A159858 Numerator of 1, 2/23, -1054/529, -6340/12167, 3332716/279841, 33496312/6436343, -17563075016/148035889, -247760738608/3404825447, 129576612091280/78310985281... %p A159858 A159858 := proc(n) %p A159858 orthopoly[H](n,1/23) ; %p A159858 numer(%) ; %p A159858 end proc: # _R. J. Mathar_, Feb 16 2014 %t A159858 Numerator[Table[HermiteH[n, 1/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *) %o A159858 (PARI) a(n)=numerator(polhermite(n,1/23)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A159858 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/23)^(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 %Y A159858 Cf. A009967 (denominators). %K A159858 sign,frac %O A159858 0,2 %A A159858 _N. J. A. Sloane_, Nov 12 2009