cp's OEIS Frontend

A158841 Triangle read by rows, matrix product of A145677 * A004736.

%I A158841 #10 May 10 2019 22:23:49
%S A158841 1,3,1,7,4,2,13,9,6,3,21,16,12,8,4,31,25,20,15,10,5,43,36,30,24,18,12,
%T A158841 6,57,49,42,35,28,21,14,7,73,64,56,48,40,32,24,16,8,91,81,72,63,54,45,
%U A158841 36,27,18,9
%N A158841 Triangle read by rows, matrix product of A145677 * A004736.
%F A158841 T(n,k) = Sum_{j=k..n} A145677(n-1,j-1)*A004736(j,k), assuming column enumeration k >= 1 in A004736. - _R. J. Mathar_, Nov 05 2011
%e A158841 First few rows of the triangle:
%e A158841     1;
%e A158841     3,   1;
%e A158841     7,   4,   2;
%e A158841    13,   9,   6,   3;
%e A158841    21,  16,  12,   8,   4;
%e A158841    31,  25,  20,  15,  10,  5;
%e A158841    43,  36,  30,  24,  18, 12,  6;
%e A158841    57,  49,  42,  35,  28, 21, 14,  7;
%e A158841    73,  64,  56,  48,  40, 32, 24, 16,  8;
%e A158841    91,  81,  72,  63,  54, 45, 36, 27, 18,  9;
%e A158841   111, 100,  90,  80,  70, 60, 50, 40, 30, 20, 10;
%e A158841   133, 121, 110,  99,  88, 77, 66, 55, 44, 33, 22, 11;
%e A158841   157, 144, 132, 120, 108, 96, 84, 72, 60, 48, 36, 24, 12;
%e A158841   ...
%p A158841 A145677 := proc(n,k)
%p A158841         if n <0 or k < 0 or k > n then
%p A158841                 0;
%p A158841         elif k = 0 then
%p A158841                 1;
%p A158841         elif k = n then
%p A158841                 n ;
%p A158841         else
%p A158841                 0 ;
%p A158841         end if;
%p A158841 end proc:
%p A158841 A004736 := proc(n,k)
%p A158841         if n <0 or k < 1 or k > n then
%p A158841                 0;
%p A158841         else
%p A158841                 n-k+1 ;
%p A158841         end if;
%p A158841 end proc:
%p A158841 A158841 := proc(n,k)
%p A158841         add( A145677(n-1,j-1)*A004736(j,k),j=k..n) ;
%p A158841 end proc: # _R. J. Mathar_, Nov 05 2011
%Y A158841 Cf. A145677, A002061 (column k=1), A158842 (row sums).
%K A158841 nonn,tabl,easy
%O A158841 1,2
%A A158841 _Gary W. Adamson_ and _Roger L. Bagula_, Mar 28 2009