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%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