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A123516
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Triangle read by rows: T(n,k)=(-1)^k*n!2^(n-2k)*binomial(n,k)binomial(2k,k) (0<=k<=n).
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0
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1, 2, -1, 8, -8, 3, 48, -72, 54, -15, 384, -768, 864, -480, 105, 3840, -9600, 14400, -12000, 5250, -945, 46080, -138240, 259200, -288000, 189000, -68040, 10395, 645120, -2257920, 5080320, -7056000, 6174000, -3333960, 1018710, -135135, 10321920, -41287680, 108380160, -180633600, 197568000
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums yield the double factorial numbers (A001147). T(n,0)=2^n*n!=A000165(n). T(n,n)=(-1)^n*A001147(n).
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REFERENCES
| B. T. Gill, Math. Magazine, vol. 79, No. 4, 2006, p. 313, problem 1729.
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MAPLE
| T:=(n, k)->(-1)^k*n!*2^(n-2*k)*binomial(n, k)*binomial(2*k, k): for n from 0 to 8 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A001147, A000165.
Sequence in context: A075733 A127674 A145901 * A193604 A016446 A086657
Adjacent sequences: A123513 A123514 A123515 * A123517 A123518 A123519
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KEYWORD
| sign,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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