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A316674 Number A(n,k) of paths from {0}^k to {n}^k that always move closer to {n}^k; square array A(n,k), n>=0, k>=0, read by antidiagonals. 6
1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 13, 26, 4, 1, 1, 75, 818, 252, 8, 1, 1, 541, 47834, 64324, 2568, 16, 1, 1, 4683, 4488722, 42725052, 5592968, 26928, 32, 1, 1, 47293, 617364026, 58555826884, 44418808968, 515092048, 287648, 64, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Antidiagonals n = 0..48, flattened

FORMULA

A(n,k) = A262809(n,k) * A011782(n) for k>0, A(n,0) = 1.

EXAMPLE

Square array A(n,k) begins:

  1,  1,     1,         1,              1,                    1, ...

  1,  1,     3,        13,             75,                  541, ...

  1,  2,    26,       818,          47834,              4488722, ...

  1,  4,   252,     64324,       42725052,          58555826884, ...

  1,  8,  2568,   5592968,    44418808968,      936239675880968, ...

  1, 16, 26928, 515092048, 50363651248560, 16811849850663255376, ...

MAPLE

A:= (n, k)-> `if`(k=0, 1, ceil(2^(n-1))*add(add((-1)^i*

     binomial(j, i)*binomial(j-i, n)^k, i=0..j), j=0..k*n)):

seq(seq(A(n, d-n), n=0..d), d=0..10);

CROSSREFS

Columns k=0-3 give: A000012, A011782, A052141, A316673.

Rows n=0-2 give: A000012, A000670, A059516.

Main diagonal gives A316677.

Cf. A011782, A262809.

Sequence in context: A316564 A214742 A204124 * A101479 A136170 A245188

Adjacent sequences:  A316671 A316672 A316673 * A316675 A316676 A316677

KEYWORD

nonn,tabl,walk

AUTHOR

Alois P. Heinz, Jul 10 2018

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)