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%I #8 May 10 2021 01:36:05
%S 1,3,6,13,32,89,276,943,3514,14159,61242,282633,1384684,7170701,
%T 39105992,223867419,1341434134,8392364851,54696456734
%N Row sums of A179927, the triangle of centered orthotopic numbers.
%C 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
%F From _Mathew Englander_, Apr 11 2021: (Start)
%F a(n) = 1 + Sum_{i = 1..n} (i+1)*i^(n-i).
%F a(n) = A026898(n) + A026898(n-1) for n > 0. (End)
%p A179928 := proc(n) local j; add(A179927(n,j),j=0..n) end;
%t 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;
%t h[n_, x_] := e[n, x] (1 + x)/(1 - x)^(n + 1);
%t T[n_, k_] := SeriesCoefficient[h[n - k, x], {x, 0, k}];
%t a[n_] := Sum[T[n, k], {k, 0, n}];
%t Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Jul 11 2019 *)
%Y Cf. A179927, A265583, A026898.
%K nonn
%O 0,2
%A _Peter Luschny_, Aug 02 2010
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