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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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EXAMPLE
| First few rows of the array are:
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
| 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
| Sequence in context: A140503 A176789 A043263 * A194998 A202864 A006047
Adjacent sequences: A118975 A118976 A118977 * A118979 A118980 A118981
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 07 2006
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2010
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