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

Author

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

Keywords

• nonn

Links

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

Crossrefs

Cf. A144502.

Programs

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

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 *)

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

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

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