A160904 Row sums of A159881.
1, 1, 1, 2, 4, 4, -5, -23, 9, 308, 1020, -448, -19647, -89379, -48935, 1958306, 13904216, 34488844, -223401589, -3022248531, -15637955831, -1081374732, 738978239768, 7071581029520, 29227771327153, -117008648911367
Offset: 0
Examples
a(1) = 2-1=1. a(2)=3-3+1=1. a(3)=4-6+5-1=2.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..594
Programs
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Maple
A159881 := proc(n,k) option remember; if k = 0 then n+1; elif k < 0 or k > n then 0 ; else k*procname(n-1,k)-procname(n-1,k-1) ; fi; end: A159881s := proc(n) add( A159881(n,k),k=0..n) ; end: seq(A159881s(n),n=0..40) ;
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Mathematica
T[n_, 0]:= n + 1; T[n_, k_]:= T[n, k] = If[k < 0 || k > n, 0, k*T[n - 1, k] - T[n - 1, k - 1]]; Table[Sum[T[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Jul 27 2018 *)
Formula
a(n) = Sum_{k=0..n} A159881(n,k).