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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, 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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

E.g.f.: exp(2*x*y)*(BesselI(0,2*x)+BesselI(1,2*x)). [From Vladeta Jovovic, 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: A243238 A169629 A231731 * A143729 A006460 A064137

Adjacent sequences:  A143355 A143356 A143357 * A143359 A143360 A143361

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 11 2008

STATUS

approved

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Last modified December 8 12:55 EST 2016. Contains 278945 sequences.