

A104856


Triangle read by rows: T(n,k) = binomial(n,k)*binomial(k,floor(k/2))*binomial(nk,floor((nk)/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
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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. [Emeric Deutsch, Nov 22 2008]


LINKS

Table of n, a(n) for n=0..57.
David M. Bloom et al., A Convolution of Middle Binomial Coefficients: Problem 10921, Amer. Math. Monthly 110, (2003), 958959.
E. Deutsch and D. Lovit, Problem 1739, Math. Magazine, vol. 80, No. 1, 2007, p. 80. [Emeric Deutsch, Nov 22 2008]


FORMULA

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


MAPLE

T:=(n, k)>binomial(n, k)*binomial(k, floor(k/2))*binomial(nk, floor((nk)/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: A341075 A193450 A109906 * A306393 A324763 A038715
Adjacent sequences: A104853 A104854 A104855 * A104857 A104858 A104859


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Apr 23 2005


STATUS

approved



