A111885 Row sums of triangle A112492.

1, 2, 5, 20, 152, 2542, 100326, 10194844, 2809233510, 2212797607312, 5359196565766782, 39928779843430949176, 1018129474625651322506886, 85890171235256453902613870992, 26477529277143069417959927152215342

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..55

Formula

a(n) = Sum_{j=0..n} A112492(n, j), n >= 0.

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, (k+1)^(n-k)*T[n-1, k-1] + k!*T[n-1, k]];
a[n_]:= a[n]= Sum[T[n, k], {k, 0, n}]; (* T = A112492 *)
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jul 24 2023 *)

Prog

(Magma)
T:= func< n, k | (-1)*Factorial(k+1)^(n-k)*(&+[(-1)^j*Binomial(k+1, j)/j^(n-k) : j in [1..k+1]]) >; // T = A112492
A111885:= func< n | (&+[T(n, k): k in [0..n]]) >;
[A111885(n): n in [0..40]]; // G. C. Greubel, Jul 24 2023
(SageMath)
@CachedFunction
def T(n, k): # T = A112492
    if (k==0 or k==n): return 1
    else: return (k+1)^(n-k)*T(n-1, k-1) + factorial(k)*T(n-1, k)
def A111885(n): return sum(T(n, k) for k in range(n+1))
[A111885(n) for n in range(31)] # G. C. Greubel, Jul 24 2023

Crossrefs

Cf. A112492.

Sequence in context: A140988 A136650 A229662 * A159320 A184730 A181076

Adjacent sequences: A111882 A111883 A111884 * A111886 A111887 A111888

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 12 2005

Status

approved