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A104856 Triangle read by rows: T(n,k)=binomial(n,k)binomial(k,floor(k/2))binomial(n-k,floor((n-k)/2)) (0<=k<=n). 0
1, 1, 1, 2, 2, 2, 3, 6, 6, 3, 6, 12, 24, 12, 6, 10, 30, 60, 60, 30, 10, 20, 60, 180, 180, 180, 60, 20, 35, 140, 420, 630, 630, 420, 140, 35, 70, 280, 1120, 1680, 2520, 1680, 1120, 280, 70, 126, 630, 2520, 5040, 7560, 7560, 5040, 2520, 630, 126, 252, 1260, 6300 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

T(n,k) is the number of paths in the first quadrant, starting from the origin, with unit steps up, down, right, or left, having a total of n steps, exactly k of which are vertical (up or down). Example: T(3,2)=6 because we have NNE, NEN, ENN, NSE, ENS and NES. [From Emeric Deutsch, Nov 22 2008]

REFERENCES

David M. Bloom, Problem 10921, Amer. Math. Monthly 110, (2003), 958-959.

E. Deutsch and D. Lovit, Math. Magazine, vol. 80, No. 1, 2007, p. 80, Problem 1739. [From Emeric Deutsch, Nov 22 2008]

LINKS

Table of n, a(n) for n=0..57.

FORMULA

T(n, k)=binomial(n, k)binomial(k, floor(k/2))binomial(n-k, floor((n-k)/2)) (0<=k<=n).

MAPLE

T:=(n, k)->binomial(n, k)*binomial(k, floor(k/2))*binomial(n-k, floor((n-k)/2)): for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

CROSSREFS

Row sums yield A005566. T(n, 0)=T(n, n)=A001405(n).

Cf. A005566, A001405.

Sequence in context: A318238 A193450 A109906 * A306393 A038715 A293518

Adjacent sequences:  A104853 A104854 A104855 * A104857 A104858 A104859

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Apr 23 2005

STATUS

approved

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Last modified February 17 14:37 EST 2019. Contains 320220 sequences. (Running on oeis4.)