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A118978
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Array read by antidiagonals: the n-th row contains the binomial transform of row n-1 of A014410.
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1
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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, 9, 36, 84, 126, 125, 74, 21, 2, 10, 45, 120, 210, 252, 205, 100, 24, 2, 11, 55, 165, 330, 462, 461, 315, 130, 27, 2, 12, 66, 220, 495, 792, 924, 786, 460, 164, 30, 2, 13, 78, 286, 715, 1287
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OFFSET
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1,1
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COMMENTS
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Each row of A014410 is extended by adding an infinite sequence of zeros,
and the binomial transform of this extended row (assuming the first term has index 0) is placed into the array here.
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LINKS
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EXAMPLE
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First few rows of the array:
2, 2, 2, 2, 2, ... (binomial transform of 2,0,0,0,0,...)
3, 6, 9, 12, 15, ... (binomial transform of 3,3,0,0,0,...)
4, 10, 20, 34, 52, ... (binomial transform of 4,6,4,0,0,...)
5, 15, 35, 70, 125, ...
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MAPLE
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read("transforms") ; A014410 := proc(n, m) if m <= n-1 and m >= 1 then binomial(n, m) ; else 0 ; end if; end proc:
A118978 := proc(n, m) L := [seq(A014410(n+1, k), k=1..m+1) ] ; BINOMIAL(L) ; op(m+1, %) ; end proc:
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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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