|
Search: id:A123516
|
|
|
| A123516 |
|
Triangle read by rows: T(n,k)=(-1)^k*n!2^(n-2k)*binomial(n,k)binomial(2k,k) (0<=k<=n). |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Row sums yield the double factorial numbers (A001147). T(n,0)=2^n*n!=A000165(n). T(n,n)=(-1)^n*A001147(n).
|
|
REFERENCES
|
B. T. Gill, Math. Magazine, vol. 79, No. 4, 2006, p. 313, problem 1729.
|
|
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
|
|
CROSSREFS
|
Cf. A001147, A000165.
Sequence in context: A021461 A127674 A075733 this_sequence A016446 A086657 A036296
Adjacent sequences: A123513 A123514 A123515 this_sequence A123517 A123518 A123519
|
|
KEYWORD
|
sign,tabl
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
|
|
|
Search completed in 0.002 seconds
|
