A118978 - OEIS

%I #8 Feb 13 2022 23:17:27

%S 2,3,2,4,6,2,5,10,9,2,6,15,20,12,2,7,21,35,34,15,2,8,28,56,70,52,18,2,

%T 9,36,84,126,125,74,21,2,10,45,120,210,252,205,100,24,2,11,55,165,330,

%U 462,461,315,130,27,2,12,66,220,495,792,924,786,460,164,30,2,13,78,286,715,1287

%N Array read by antidiagonals: the n-th row contains the binomial transform of row n-1 of A014410.

%C Each row of A014410 is extended by adding an infinite sequence of zeros,

%C and the binomial transform of this extended row (assuming the first term has index 0) is placed into the array here.

%e First few rows of the array:

%e   2,  2,  2,  2,   2, ... (binomial transform of 2,0,0,0,0,...)

%e   3,  6,  9, 12,  15, ... (binomial transform of 3,3,0,0,0,...)

%e   4, 10, 20, 34,  52, ... (binomial transform of 4,6,4,0,0,...)

%e   5, 15, 35, 70, 125, ...

%p read("transforms") ; A014410 := proc(n,m) if m <= n-1 and m >= 1 then binomial(n,m) ; else 0 ; end if; end proc:

%p A118978 := proc(n,m) L := [seq(A014410(n+1,k),k=1..m+1) ] ; BINOMIAL(L) ; op(m+1,%) ; end proc:

%p for d from 1 to 20 do for m from 0 to d-1 do printf("%d,", A118978(d-m,m)) ; end do: printf("\n") ; end do; # _R. J. Mathar_, Jun 15 2010

%K nonn,tabl

%O 1,1

%A _Gary W. Adamson_, May 07 2006

%E Edited and extended by _R. J. Mathar_, Jun 15 2010