OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(0,0) = 1, T(n,k) = (Sum_{j=0..n} j*C(2*n-j-1,n-j) * C(j,k) * 2^(n-j))/n.
T(n,k) = (-1)^(n-k)*A114189(n,k). - Philippe Deléham, Mar 24 2007
EXAMPLE
Rows begin:
1;
1,1;
3,4,1;
13,19,7,1;
67,102,44,10,1;
381,593,278,78,13,1;
From Philippe Deléham, Dec 01 2015: (Start)
Production matrix begins:
1, 1
2, 3, 1
2, 4, 3, 1
2, 4, 4, 3, 1
2, 4, 4, 4, 3, 1
2, 4, 4, 4, 4, 3, 1
2, 4, 4, 4, 4, 4, 3, 1
(End)
MATHEMATICA
{{1}}~Join~Table[Sum[j Binomial[2 n - j - 1, n - j] Binomial[j, k] 2^(n - j), {j, 0, n}]/n, {n, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Dec 01 2015 *)
PROG
(PARI) tabl(nn)= {for (n=0, nn, for (k=0, n, if (n==0, x = 0^k, x = sum(j=0, n, j*binomial(2*n-j-1, n-j)*binomial(j, k)*2^(n-j)/n)); print1(x, ", "); ); print(); ); } \\ Michel Marcus, Jun 18 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jul 24 2005
STATUS
approved