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A080248
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Stirling-like number triangle defined by sequence A000217.
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2
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1, 1, 1, 1, 4, 1, 1, 13, 10, 1, 1, 40, 73, 20, 1, 1, 121, 478, 273, 35, 1, 1, 364, 2989, 3208, 798, 56, 1, 1, 1093, 18298, 35069, 15178, 1974, 84, 1, 1, 3280, 110881, 368988, 262739, 56632, 4326, 120, 1, 1, 9841, 668566, 3800761, 4310073, 1452011, 177760
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Columns include A003462, A016211, A021514. The defining sequence A000217(n)=C(n+1,2) is the sequence of partial sums of the sequence (0,1,2,3,4,....) which defines the Stirling numbers of the second kind A008277.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009: (Start)
n-th row = M^n * [1,0,0,0,...], where M = an infinite lower triangular matrix
with (1, 3, 6,...) in the main diagonal and (1, 1, 1,...) in the subdiagonal. (End)
Row sums = A124373 starting (1, 2, 6, 25, 135,...) - Gary W. Adamson, Jul 11 2011
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FORMULA
| Columns are generated by 1/product{k=1, .., n+1, 1-C(k+1, 2)x}
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EXAMPLE
| Rows are {1}, {1,1}, {1,4,1}, {1, 13, 10, 1}, {1,40, 73, 20, 1}, ... For example, 73 = 13+6.10, 20 = 10+10.1
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PROG
| (PARI) T(n, k)=local(s); if(k<0|k>n, 0, forvec(v=vector(n-k, i, [0, k]), s+=prod(i=1, n-k, v[i]*(v[i]+1)/2), 1)); s - Michael Somos Feb 06 2004
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CROSSREFS
| Cf. A000217, A008277.
Cf. A124373
Sequence in context: A101275 A039755 A047874 * A139382 A157180 A179086
Adjacent sequences: A080245 A080246 A080247 * A080249 A080250 A080251
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 17 2003
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