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A134836 Antidiagonals of the array: A007318 * A002260(transposed).

%I A134836 #11 May 21 2025 19:01:19
%S A134836 1,1,1,1,3,1,1,5,3,1,1,7,8,3,1,1,9,16,8,3,1,1,11,27,20,8,3,1,1,13,41,
%T A134836 43,20,8,3,1,1,15,58,81,48,20,8,3,1,1,17,78,138,106,48,20,8,3,1,1,19,
%U A134836 101,218,213,112,48,20,8,3,1
%N A134836 Antidiagonals of the array: A007318 * A002260(transposed).
%C A134836 Antidiagonals tend to A001792 starting from the right: (1, 3, 8, 20, 48, 112, ...).
%F A134836 Antidiagonals of the array: A007318 * A002260(transform), where A002260 = (1; 1,2; 1,2,3; ...).
%e A134836 First few rows of the array:
%e A134836   1,  1,  1,  1,   1,   1, ...;
%e A134836   1,  3,  3,  3,   3,   3, ...;
%e A134836   1,  5,  8,  8,   8,   8, ...;
%e A134836   1,  7, 16, 20,  20,  20, ...;
%e A134836   1,  9, 27, 43,  48,  48, ...;
%e A134836   1, 11, 41, 81, 106, 112, ...;
%e A134836   ...
%e A134836 First few rows of the triangle:
%e A134836   1;
%e A134836   1,  1;
%e A134836   1,  3,  1;
%e A134836   1,  5,  3,  1;
%e A134836   1,  7,  8,  3,  1;
%e A134836   1,  9, 16,  8,  3,  1;
%e A134836   1, 11, 27, 20,  8,  3,  1;
%e A134836   1, 13, 41, 43, 20,  8,  3,  1;
%e A134836   ...
%p A134836 A002260 := proc(n,k)
%p A134836     if n <= k then
%p A134836         n+1;
%p A134836     else
%p A134836         0 ;
%p A134836     end if;
%p A134836 end proc:
%p A134836 A007318 := proc(n,k)
%p A134836     if k <= n then
%p A134836         binomial(n,k) ;
%p A134836     else
%p A134836         0
%p A134836     end if;
%p A134836 end proc:
%p A134836 A134836 := proc(n,k)
%p A134836     add( A007318(n,i)*A002260(i,k),i=0..k) ;
%p A134836 end proc:
%p A134836 seq(seq(A134836(d-k,k),k=0..d),d=0..12) ; # _R. J. Mathar_, Aug 17 2022
%Y A134836 Cf. A002260, A001792, A116445 (array transposed), A001629 (antidiagonal sums).
%K A134836 nonn,tabl,easy
%O A134836 1,5
%A A134836 _Gary W. Adamson_, Nov 12 2007
%E A134836 One term corrected by _R. J. Mathar_, Aug 17 2022