OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
FORMULA
Sum_{k=0..n} T(n,k)*x^k = A126869(n), A002426(n), A000984(n), A026375(n), A081671(n), A098409(n), A098410(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively. - Philippe Deléham, Sep 28 2007
T(n,k) = binomial(n,k)*A000984(n-k). - Philippe Deléham, Dec 12 2009
O.g.f.: 1/sqrt( (1 - x*t)*(1 - (x + 4)*t) ) = 1 + (2 + x)*t + (6 + 4*x + x^2)*t^2 + .... - Peter Bala, Nov 10 2013
EXAMPLE
Triangle begins:
1;
2, 1;
6, 4, 1;
20, 18, 6, 1;
70, 80, 36, 8, 1;
252, 350, 200, 60, 10, 1;
...
MAPLE
c:=n->binomial(2*n, n): T:=proc(n, k) if k<=n then binomial(n, k)*c(n-k) else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; #
MATHEMATICA
Table[ Binomial[n, k]*Binomial[2*n - 2*k, n - k], {n, 0, 10}, {k, 0, n} ] // Flatten (* G. C. Greubel, Mar 07 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Farkas Janos Smile (smile_farkasjanos(AT)yahoo.com.au), Dec 21 2006
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 12 2007
STATUS
approved