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Search: id:A049020
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| A049020 |
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Triangle of numbers a(n,k), 0<=k<=n, related to Bell numbers. |
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+0
11
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| 1, 1, 1, 2, 3, 1, 5, 10, 6, 1, 15, 37, 31, 10, 1, 52, 151, 160, 75, 15, 1, 203, 674, 856, 520, 155, 21, 1, 877, 3263, 4802, 3556, 1400, 287, 28, 1, 4140, 17007, 28337, 24626, 11991, 3290, 490, 36, 1, 21147, 94828, 175896, 174805, 101031, 34671, 6972, 786
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Triangle a(n,k) read by rows; given by [1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1,...] DELTA [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...] where DELTA is Deleham's operator defined in A084938.
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REFERENCES
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M. Aigner, A characterization of the Bell numbers, Discr. Math., 205 (1999), 207-210.
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FORMULA
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a(n, k)=a(n-1, k-1)+(k+1)*a(n-1, k)+(k+1)*a(n-1, k+1), n >= 1.
a(n, k)=Sum_{i=0..n} stirling2(n, i)*binomial(i, k), k=0..n. E.g.f. for k-th column is (1/k!) *(exp(x)-1)^k*exp(exp(x)-1) - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 27 2001
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EXAMPLE
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1; 1,1; 2,3,1; 5,10,6,1; 15,37,31,10,1; ...
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PROGRAM
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(PARI) T(n, k)=if(k<0|k>n, 0, n!*polcoeff(polcoeff(exp((1+y)*(exp(x+x*O(x^n))-1)), n), k))
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CROSSREFS
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First column gives A000110, second column = A005493.
Third column = A003128, row sums = A001861, A059340.
Sequence in context: A090299 A060693 A089302 this_sequence A085853 A137211 A083855
Adjacent sequences: A049017 A049018 A049019 this_sequence A049021 A049022 A049023
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KEYWORD
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nonn,tabl,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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