A138767 Triangle read by rows: T(n,k) = binomial(n,k)*binomial(2*n-2*k,n-1), n>=1, 0<=k<=floor(n/2+1/2).

1, 1, 4, 4, 15, 18, 3, 56, 80, 24, 210, 350, 150, 10, 792, 1512, 840, 120, 3003, 6468, 4410, 980, 35, 11440, 27456, 22176, 6720, 560, 43758, 115830, 108108, 41580, 5670, 126, 167960, 486200, 514800, 240240, 46200, 2520

Offset

1,3

Comments

Row n contains floor(n/2+3/2) terms.

Row sums with alternate signs are 0.

Links

Table of n, a(n) for n=1..40.

D. Beckwith, A Vanishing Alternating Sum: Problem 11212/11220, Amer. Math. Monthly 115, (2008), p. 366.

Example

Triangle starts:
1,1;
4,4;
15,18,3;
56,18,3;
210,350,150,10;

Maple

T:=proc(n, r) options operator, arrow: binomial(n, r)*binomial(2*n-2*r, n-1) end proc: for n to 10 do seq(T(n, k), k=0..floor((1/2)*n+1/2)) end do; # yields sequence in triangular form

Crossrefs

Sequence in context: A271546 A325655 A117187 * A048282 A068592 A198313

Adjacent sequences: A138764 A138765 A138766 * A138768 A138769 A138770

Keyword

nonn,tabf

Author

Emeric Deutsch, Mar 30 2008

Status

approved