cp's OEIS Frontend

A129687 A129686 * A007318.

%I A129687 #9 Feb 20 2022 01:26:41
%S A129687 1,1,1,2,2,1,2,4,3,1,2,6,7,4,1,2,8,13,11,5,1,2,10,21,24,16,6,1,2,12,
%T A129687 31,45,40,22,7,1,2,14,43,76,85,62,29,8,1,2,16,57,119,161,147,91,37,9,
%U A129687 1,2,18,73,176,280,308,238,128,46,10,1,2,20,91,249,456
%N A129687 A129686 * A007318.
%C A129687 Row sums = A084215: (1, 2, 5, 10, 20, 40, 80, ...). A007318 * A129686 = A124725.
%C A129687 From _Philippe Deléham_, Feb 12 2014: (Start)
%C A129687 Riordan array ((1+x^2)/(1-x), x/(1-x)).
%C A129687 Diagonal sums are A000032(n) - 0^n (cf. A000204).
%C A129687 T(n,0) = A046698(n+1).
%C A129687 T(n+1,1) = A004277(n).
%C A129687 T(n+2,2) = A002061(n+1).
%C A129687 T(n+3,3) = A006527(n+1) = A167875(n).
%C A129687 T(n+4,4) = A006007(n+1).
%C A129687 T(n+5,5) = A081282(n+1). (End)
%F A129687 A129686 * A007318 (Pascal's Triangle), as infinite lower triangular matrices.
%F A129687 T(n,k) = T(n-1,k) + T(n-1,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Feb 12 2014
%e A129687 First few rows of the triangle:
%e A129687   1;
%e A129687   1,   1;
%e A129687   2,   2,   1;
%e A129687   2,   4,   3,   1;
%e A129687   2,   6,   7,   4,   1;
%e A129687   2,   8,  13,  11,   5,   1;
%e A129687   2,  10,  21,  24,  16,   6,   1;
%e A129687   2,  12,  31,  45,  40,  22,   7,   1;
%e A129687   2,  14,  43,  76,  85,  62,  29,   8,   1;
%e A129687   2,  16,  57, 119, 161, 147,  91,  37,   9,   1;
%e A129687   ...
%Y A129687 Cf. A129686, A007318, A124725.
%Y A129687 Cf. Columns: A046698, A004277, A002061, A006527, A006007, A081282
%K A129687 nonn,tabl
%O A129687 0,4
%A A129687 _Gary W. Adamson_, Apr 28 2007
%E A129687 More terms from _Philippe Deléham_, Feb 12 2014