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Search: id:A082137
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| A082137 |
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Square array of transforms of binomial coefficients, read by antidiagonals. |
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+0
12
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| 1, 1, 1, 1, 2, 2, 1, 3, 6, 4, 1, 4, 12, 16, 8, 1, 5, 20, 40, 40, 16, 1, 6, 30, 80, 120, 96, 32, 1, 7, 42, 140, 280, 336, 224, 64, 1, 8, 56, 224, 560, 896, 896, 512, 128, 1, 9, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 1, 10, 90, 480, 1680, 4032, 6720, 7680, 5760, 2560, 512
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows are associated with the expansions of (x^k/k!)exp(x)cosh(x) (leading zeros dropped). Rows include A011782, A057711, A080929, A082138, A080951, A082139, A082140, A082141. Columns are of the form 2^(k-1)C(n+k, k). Diagonals include A092246, A082143, A082144, A082145, A069720.
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LINKS
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A. Laradji and A. Umar, Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.8.
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FORMULA
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Square array defined by T(n, k)=(2^(n-1)+0^n/2)C(n + k, n)= Sum{k=0..n, C(n+k, k+j)C(k+j, k)(1+(-1)^j)/2 }
As an infinite lower triangular matrix, equals A007318 * A134309. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007
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EXAMPLE
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Rows begin
1 1 2 4 8 ...
1 2 6 16 40 ...
1 3 12 40 120 ...
1 4 20 80 280 ...
1 5 30 140 560 ...
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CROSSREFS
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Cf. A007318.
Cf. A134309.
Sequence in context: A094441 A107230 A046726 this_sequence A091187 A065173 A098474
Adjacent sequences: A082134 A082135 A082136 this_sequence A082138 A082139 A082140
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 06 2003
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