A179928 Row sums of A179927, the triangle of centered orthotopic numbers.

1, 3, 6, 13, 32, 89, 276, 943, 3514, 14159, 61242, 282633, 1384684, 7170701, 39105992, 223867419, 1341434134, 8392364851, 54696456734

Offset: 0

Author

Peter Luschny, Aug 02 2010

Keywords

• nonn

Comments

a(n)-1 is the sum of the antidiagonal of array A265583 from (n+1,1) to (1,n+1). - Mathew Englander, Apr 11 2021

Crossrefs

Cf. A179927, A265583, A026898.

Programs

Maple

A179928 := proc(n) local j; add(A179927(n,j),j=0..n) end;

Mathematica

e[0, ] = 1; e[n, x_] := e[n, x] = x (1 - x) D[e[n - 1, x], x] + e[n - 1, x] (1 + (n - 1) x) // Expand;
h[n_, x_] := e[n, x] (1 + x)/(1 - x)^(n + 1);
T[n_, k_] := SeriesCoefficient[h[n - k, x], {x, 0, k}];
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Jul 11 2019 *)

Formula

From Mathew Englander, Apr 11 2021: (Start)

a(n) = 1 + Sum_{i = 1..n} (i+1)*i^(n-i).

a(n) = A026898(n) + A026898(n-1) for n > 0. (End)