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A143358
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Triangle read by rows: T(n,k) = 2^k*binomial(n,k)*binomial(n-k, floor((n-k)/2)), 0 <= k <= n.
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1
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1, 1, 2, 2, 4, 4, 3, 12, 12, 8, 6, 24, 48, 32, 16, 10, 60, 120, 160, 80, 32, 20, 120, 360, 480, 480, 192, 64, 35, 280, 840, 1680, 1680, 1344, 448, 128, 70, 560, 2240, 4480, 6720, 5376, 3584, 1024, 256, 126, 1260, 5040, 13440, 20160, 24192, 16128, 9216, 2304, 512
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OFFSET
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0,3
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COMMENTS
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Sum of terms in row n = binomial(2n+1,n) (A001700; see the Andreescu-Feng reference).
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REFERENCES
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T. Andreescu and Z. Feng, 102 Combinatorial Problems (from the training of the USA IMO team), Birkhauser, Boston, 2003, Advanced problem # 15, pp. 11,61-63.
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LINKS
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FORMULA
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E.g.f.: exp(2*x*y)*(BesselI(0,2*x) + BesselI(1,2*x)). - Vladeta Jovovic, Dec 02 2008
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EXAMPLE
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Triangle begins:
1;
1, 2;
2, 4, 4;
3, 12, 12, 8;
6, 24, 48, 32, 16;
10, 60, 120, 160, 80, 32;
...
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MAPLE
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T:=proc(n, k) options operator, arrow: 2^k*binomial(n, k)*binomial(n-k, floor((1/2)*n-(1/2)*k)) end proc: for n from 0 to 9 do seq(T(n, k), k=0..n) end do; # yields sequence in triangular form
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MATHEMATICA
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Flatten[Table[2^k Binomial[n, k]Binomial[n-k, Floor[(n-k)/2]], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jun 28 2021 *)
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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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