A144503 Sum of n-th antidiagonal of array in A144502.

1, 2, 5, 20, 121, 982, 9933, 120168, 1692273, 27196522, 491229653, 9851789564, 217230600041, 5223386190526, 136025271553693, 3813930989693904, 114553954962370785, 3669540489785558994, 124878930607671376549, 4499311042365955114724, 171098698540513965736025

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..404

Formula

a(n) ~ sqrt(Pi) * 2^(n - 1/2) * n^(n - 1/2) / exp(n-1). - Vaclav Kotesovec, Apr 06 2019

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

Mathematica

a[n_]:= a[n]= If[n<2, n+1, 2*(n-1)*a[n-1] +a[n-2] -2*(n-2)];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 09 2023 *)

Prog

(Ruby)
def A144503(n)
  ary = []
  a = [1]
  (n + 1).times{|i|
    (1..i).each{|j|
      a[j] *= i - j
      a[j] += a[j - 1]
    }
    ary << a.inject(:+)
    a << 0
  }
  ary
end
p A144503(20) # Seiichi Manyama, Apr 06 2019
(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
(SageMath)
@CachedFunction
def a(n): # A144503
    if (n<2): return n+1
    else: return 2*(n-1)*a(n-1) + a(n-2) - 2*(n-2)
[a(n) for n in range(31)] # G. C. Greubel, Oct 09 2023

Crossrefs

Cf. A144502.

Sequence in context: A288841 A009599 A112833 * A012321 A012519 A076795

Adjacent sequences: A144500 A144501 A144502 * A144504 A144505 A144506

Keyword

nonn

Author

David Applegate and N. J. A. Sloane, Dec 13 2008

Status

approved