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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 (list; table; graph; refs; listen; history; text; internal format)
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: A323936 A305839 A322110 * A289006 A152167 A105476

Adjacent sequences:  A232970 A232971 A232972 * A232974 A232975 A232976

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Dec 05 2013

EXTENSIONS

a(15)-a(38) from Lars Blomberg, Jul 20 2017

STATUS

approved

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Last modified March 19 13:25 EDT 2019. Contains 321330 sequences. (Running on oeis4.)