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

0,2

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

Links

Table of n, a(n) for n=0..18.

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)

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 *)

Crossrefs

Cf. A179927, A265583, A026898.

Sequence in context: A162483 A187780 A273974 * A026538 A358454 A361932

Adjacent sequences: A179925 A179926 A179927 * A179929 A179930 A179931

Keyword

nonn

Author

Peter Luschny, Aug 02 2010

Status

approved