|
Search: id:A143358
|
|
|
| A143358 |
|
Triangle read by rows: T(n,k)=2^k*binom(n,k)binom(n-k, floor((n-k)/2)), 0<=k<=n. |
|
+0
1
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Sum of terms in row n = binom(2n+1,n) (A001700; see the Andreescu-Feng reference).
|
|
REFERENCES
|
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.
|
|
FORMULA
|
E.g.f.: exp(2*x*y)*(BesselI(0,2*x)+BesselI(1,2*x)). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Dec 02 2008]
|
|
MAPLE
|
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
|
|
CROSSREFS
|
Cf. A001700.
Sequence in context: A024222 A110545 A104798 this_sequence A143729 A006460 A064137
Adjacent sequences: A143355 A143356 A143357 this_sequence A143359 A143360 A143361
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 11 2008
|
|
|
Search completed in 0.002 seconds
|
