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A232973
Dziemianczuk's array S(i,j) read by antidiagonals.
3
1, 3, 6, 15, 33, 60, 81, 189, 378, 675, 459, 1107, 2349, 4509, 7992, 2673, 6588, 14553, 29403, 55188, 97416, 15849, 39663, 90207, 189351, 371358, 687258, 1209951, 95175, 240894, 560115, 1211031, 2458998, 4727565, 8664813, 15227190, 576963, 1473147, 3485187
OFFSET
0,2
LINKS
Lars Blomberg, Table of n, a(n) for n = 0..5049 (The first 100 antidiagonals)
M. Dziemianczuk, Counting Lattice Paths With Four Types of Steps, Graphs and Combinatorics, September 2013, DOI 10.1007/s00373-013-1357-1.
EXAMPLE
Array begins:
1, 3, 15, 81, 459, 2673, 15849, ...
6, 33, 189, 1107, 6588, 39663, 240894, ...
60, 378, 2349, 14553, 90207, 560115, 3485187, ...
675, 4509, 29403, 189351, 1211031, 7715331, 49045662, ...
7992, 55188, 371358, 2458998, 16112925, 104838219, 678790125, ...
...
PROG
(PARI) \\ Dziemianczuk, Proposition 1
S(n, k)=sum(i=0, n+k, sum(j=0, i, binomial(k, j)*binomial(j, i-j)*binomial(2*k+n-i, k)));
A=[]; for(i=1, 10, A=concat(A, vector(i, j, S(j-1, i-1))));
A \\ Lars Blomberg, Jul 20 2017
CROSSREFS
See A122868 and A232969 for leading row row and column.
Sequence in context: A305839 A322110 A375617 * A289006 A336632 A152167
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 05 2013
EXTENSIONS
a(15)-a(38) from Lars Blomberg, Jul 20 2017
STATUS
approved