OFFSET
0,3
COMMENTS
Sum of terms in row n = binomial(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
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
E.g.f.: exp(2*x*y)*(BesselI(0,2*x) + BesselI(1,2*x)). - Vladeta Jovovic, Dec 02 2008
EXAMPLE
Triangle begins:
1;
1, 2;
2, 4, 4;
3, 12, 12, 8;
6, 24, 48, 32, 16;
10, 60, 120, 160, 80, 32;
...
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
MATHEMATICA
Flatten[Table[2^k Binomial[n, k]Binomial[n-k, Floor[(n-k)/2]], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jun 28 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 11 2008
STATUS
approved