cp's OEIS Frontend

A281334 Triangle read by rows: T(n, k) = (n - k)*(k + 1)^3 + k, 0 <= k <= n.

%I A281334 #38 Sep 08 2022 08:46:18
%S A281334 0,1,1,2,9,2,3,17,29,3,4,25,56,67,4,5,33,83,131,129,5,6,41,110,195,
%T A281334 254,221,6,7,49,137,259,379,437,349,7,8,57,164,323,504,653,692,519,8,
%U A281334 9,65,191,387,629,869,1035,1031,737,9,10,73,218,451,754,1085,1378,1543,1466,1009,10
%N A281334 Triangle read by rows: T(n, k) = (n - k)*(k + 1)^3 + k, 0 <= k <= n.
%F A281334 Row sums sum_{k>=0} T(n,k) = n*(n+1)*(3*n^3+12*n^2+13*n+32)/60. - _R. J. Mathar_, Mar 19 2017
%e A281334 Triangle begins:
%e A281334    0;
%e A281334    1,    1;
%e A281334    2,    9,    2;
%e A281334    3,   17,   29,    3;
%e A281334    4,   25,   56,   67,    4;
%e A281334    5,   33,   83,  131,  129,    5;
%e A281334    6,   41,  110,  195,  254,  221,    6;
%e A281334    7,   49,  137,  259,  379,  437,  349,    7;
%e A281334    8,   57,  164,  323,  504,  653,  692,  519,    8;
%e A281334    9,   65,  191,  387,  629,  869, 1035, 1031,  737,    9;
%e A281334   10,   73,  218,  451,  754, 1085, 1378, 1543, 1466, 1009,   10;
%e A281334   ...
%t A281334 t[n_, k_] := (n - k)*(k + 1)^3 + k; Table[ t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Robert G. Wilson v_, Feb 09 2017 *)
%o A281334 (Magma) /* As triangle */ [[(n-k)*(k+1)^3+k: k in [1..n]]: n in [0..10]];
%o A281334 (PARI) for(n=0,10,for(k=0,n,print1((n-k)*(k+1)^3+k,", "))) \\ _Derek Orr_, Feb 26 2017
%Y A281334 Cf. Triangle read by rows: T(n,k) = (n-k)*(k+1)^m+k: A003056 (m = 0), A059036 (m = 1), A274602 (m = 2), this sequence (m = 3).
%Y A281334 Cf. A001477 (column 0), A017077 (column 1), A281546 (column 2), A242604 (middle diagonal).
%K A281334 nonn,tabl,easy
%O A281334 1,4
%A A281334 _Juri-Stepan Gerasimov_, Jan 23 2017