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A213853
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Rectangular array: (row n) = b**c, where b(h) = h, c(h) = binomial(2*n-4+2*h,n-2+h), n>=1, h>=1, and ** = convolution.
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2
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1, 4, 2, 13, 10, 6, 42, 38, 32, 20, 141, 136, 128, 110, 70, 492, 486, 476, 452, 392, 252, 1767, 1760, 1748, 1718, 1638, 1428, 924, 6474, 6466, 6452, 6416, 6316, 6036, 5280, 3432, 24051, 24042, 24026, 23984, 23864
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OFFSET
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1,2
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COMMENTS
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Row 1, (1,2,3,4,5,...)**(1,2,6,20,70,...):
Row 2, (1,2,3,4,5,...)**(2,6,20,70,252,...):
Row 3, (1,2,3,4,5,...)**(6,20,70,252,...):
For a guide to related arrays, see A213500.
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LINKS
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EXAMPLE
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Northwest corner (the array is read by falling antidiagonals):
1....4.....13.....42.....141
2....10....38.....136....486
6....32....128....476....1748
20...110...452....1718...6416
70...392...1638...6316...23864
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MATHEMATICA
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b[n_]:=n; c[n_]:=Binomial[2n-2, n-1
t[n_, k_]:=Sum[b[k-i]c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:=Table[t[n, k], {k, 1, 20}] (* A213853 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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