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
FORMULA
From Mathew Englander, Apr 11 2021: (Start)
a(n) = 1 + Sum_{i = 1..n} (i+1)*i^(n-i).
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 02 2010
STATUS
approved