cp's OEIS Frontend

A127718 A007318 * A002260 as infinite lower triangular matrices; A002260 = [1; 1,2; 1,2,3; ...].

%I A127718 #11 Feb 08 2022 20:20:24
%S A127718 1,2,2,4,6,3,8,14,12,4,16,30,33,20,5,32,62,78,64,30,6,64,126,171,168,
%T A127718 110,42,7,128,254,360,396,320,174,56,8,256,510,741,876,815,558,259,72,
%U A127718 9,512,1022,1506,1864,1910,1536,910,368,90,10,1024,2046,3039,3872,4240
%N A127718 A007318 * A002260 as infinite lower triangular matrices; A002260 = [1; 1,2; 1,2,3; ...].
%C A127718 Binomial transform of A002260.
%C A127718 Row sums = A084851: (1, 4, 13, 38, 104, 272, ...) A002260 * A007318 = A127717.
%F A127718 T(n,k) = Sum_{i=1..n} A007318(n-1,i-1)*A002260(i,k). - _R. J. Mathar_, Oct 02 2007
%e A127718 First few rows of the triangle:
%e A127718    1;
%e A127718    2,   2;
%e A127718    4,   6,   3;
%e A127718    8,  14,  12,   4;
%e A127718   16,  30,  33,  20,   5;
%e A127718   32,  62,  78,  64,  30,  6;
%e A127718   64, 126, 171, 168, 110, 42, 7;
%e A127718   ...
%p A127718 A007318 := proc(n,k) binomial(n,k) ; end: A002260 := proc(n,k) if k <= n then k; else 0 ; fi ; end: A127718 := proc(n,k) add( A007318(n-1,i-1)*A002260(i,k),i=1..n) ; end: for n from 1 to 15 do for k from 1 to n do printf("%d,",A127718(n,k)) ; od: od: # _R. J. Mathar_, Oct 02 2007
%Y A127718 Cf. A002260, A007318, A084851, A127717.
%K A127718 nonn,tabl,easy
%O A127718 1,2
%A A127718 _Gary W. Adamson_, Jan 25 2007
%E A127718 More terms from _R. J. Mathar_, Oct 02 2007