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A127899 (unsigned) * A004736.
2

%I #9 Mar 14 2017 00:13:30

%S 1,6,2,15,9,3,28,20,12,4,45,35,25,15,5,66,54,42,30,18,6,91,77,63,49,

%T 35,21,7,120,104,88,72,56,40,24,8,153,135,117,99,81,63,45,27,9,190,

%U 170,150,130,110,90,70,50,30,10

%N A127899 (unsigned) * A004736.

%C Row sums = the cubes, A000578: (1, 8, 27, 64, 125, ...). Left column = the hexagonal numbers: A000384: (1, 6, 15, 28, ...). A128226 = A004736 * A127899.

%F A127899 (unsigned) * A004736, as infinite lower triangular matrices. Triangle read by rows: n*[(1); (3,1); (5,3,1);...]; cf. A099375.

%e First few rows of the triangle are:

%e 1;

%e 6, 2;

%e 15, 9, 3;

%e 28, 20, 12, 4;

%e 45, 35, 25, 15, 5;

%e 66, 54, 42, 30, 18, 6;

%e 91, 77, 63, 49, 35, 21, 7;

%e ...

%t (* a127899U computes the unsigned version of A127899 *)

%t a127899U[n_, k_] := If[n==k||n-1==k, n, 0]/;(1<=k<=n)

%t a004736[n_, k_] := n-k+1/;(1<=k<=n+1)

%t a128225[n_, k_] := a127899U[n, n](a004736[n, k] + a004736[n-1, k])/;(1<=k<=n)

%t a128225[r_] := Table[a128225[n, k], {n, 1, r}, {k, 1, n}]

%t TableForm[a128225[7]] (* triangle *)

%t Flatten[a128225[10]] (* data *) (* _Hartmut F. W. Hoft_, Mar 13 2017 *)

%Y Cf. A000384, A000578, A004736, A099375, A127899, A128226.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Feb 19 2007