cp's OEIS Frontend

A208656 Triangle T(n, k) = n*C(n,k) - C(n-1,k-1), 1 <= k <= n, read by rows.

%I A208656 #10 Feb 01 2022 15:26:15
%S A208656 0,3,1,8,7,2,15,21,13,3,24,46,44,21,4,35,85,110,80,31,5,48,141,230,
%T A208656 225,132,43,6,63,217,427,525,413,203,57,7,80,316,728,1078,1064,700,
%U A208656 296,73,8,99,441,1164,2016,2394,1974,1116,414,91,9,120,595,1770
%N A208656 Triangle T(n, k) = n*C(n,k) - C(n-1,k-1), 1 <= k <= n, read by rows.
%C A208656 Mirror of A208657.
%C A208656 col 1:  A005563
%C A208656 col 2:  A127736
%C A208656 top edge:  A000027
%e A208656 First five rows:
%e A208656 0
%e A208656 3....1
%e A208656 8....7....2
%e A208656 15...21...13...3
%e A208656 24...46...44...21...4
%t A208656 z = 12;
%t A208656 f[n_, k_] := n*Binomial[n, k] - Binomial[n - 1, k - 1]
%t A208656 t = Table[f[n, k], {n, 1, z}, {k, 1, n}];
%t A208656 TableForm[t] (* A208656 as a triangle *)
%t A208656 Flatten[t]   (* A208656 as a sequence *)
%t A208656 r = Table[f[n, k], {n, 1, z}, {k, n, 1, -1}];
%t A208656 TableForm[r] (* A208657 as a triangle *)
%t A208656 Flatten[r]   (* A208657 as a sequence *)
%t A208656 Table[Sum[f[n, k], {k, 1, n}], {n, 1, 3 z}](* A208658 *)
%Y A208656 Cf. A208657, A208658.
%K A208656 nonn,tabl
%O A208656 1,2
%A A208656 _Clark Kimberling_, Mar 01 2012
%E A208656 Definition amended by _Georg Fischer_, Feb 01 2022