A144503 - OEIS

%I #18 Oct 10 2023 05:05:04

%S 1,2,5,20,121,982,9933,120168,1692273,27196522,491229653,9851789564,

%T 217230600041,5223386190526,136025271553693,3813930989693904,

%U 114553954962370785,3669540489785558994,124878930607671376549,4499311042365955114724,171098698540513965736025

%N Sum of n-th antidiagonal of array in A144502.

%H Seiichi Manyama, <a href="/A144503/b144503.txt">Table of n, a(n) for n = 0..404</a>

%F a(n) ~ sqrt(Pi) * 2^(n - 1/2) * n^(n - 1/2) / exp(n-1). - _Vaclav Kotesovec_, Apr 06 2019

%F a(n) = 2*(n-1)*a(n-1) + a(n-2) - 2*(n-2), with a(0) = 1, a(1) = 2. - _G. C. Greubel_, Oct 09 2023

%t a[n_]:= a[n]= If[n<2, n+1, 2*(n-1)*a[n-1] +a[n-2] -2*(n-2)];

%t Table[a[n], {n,0,30}] (* _G. C. Greubel_, Oct 09 2023 *)

%o (Ruby)

%o def A144503(n)

%o   ary = []

%o   a = [1]

%o   (n + 1).times{|i|

%o     (1..i).each{|j|

%o       a[j] *= i - j

%o       a[j] += a[j - 1]

%o     }

%o     ary << a.inject(:+)

%o     a << 0

%o   }

%o   ary

%o end

%o p A144503(20) # _Seiichi Manyama_, Apr 06 2019

%o (Magma) [n le 2 select n else 2*(n-2)*Self(n-1) +Self(n-2) -2*(n-3): n in [1..30]]; // _G. C. Greubel_, Oct 09 2023

%o (SageMath)

%o @CachedFunction

%o def a(n): # A144503

%o     if (n<2): return n+1

%o     else: return 2*(n-1)*a(n-1) + a(n-2) - 2*(n-2)

%o [a(n) for n in range(31)] # _G. C. Greubel_, Oct 09 2023

%Y Cf. A144502.

%K nonn

%O 0,2

%A _David Applegate_ and _N. J. A. Sloane_, Dec 13 2008