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A064045 Square array read by antidiagonals of number of length 2k walks on an n-dimensional hypercubic lattice starting and finishing at the origin and staying in the nonnegative part. 2
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 10, 3, 1, 0, 14, 70, 24, 4, 1, 0, 42, 588, 285, 44, 5, 1, 0, 132, 5544, 4242, 740, 70, 6, 1, 0, 429, 56628, 73206, 16016, 1525, 102, 7, 1, 0, 1430, 613470, 1403028, 410928, 43470, 2730, 140, 8, 1, 0, 4862, 6952660, 29082339 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..58.

R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6

FORMULA

a(n, k) = sum{j = 0, ..., k}[C(2k, 2j)c(j)a(n-1, k-j)] where c(j) = C(2j, j)/(j+1) = A000108(j) with a(0, 0) = 1

EXAMPLE

Rows start: {1, 0, 0, 0, 0, 0, 0,...}, {1, 1, 2, 5, 14, 42, 132,...}, {1, 2, 10, 70, 588, 5544, 56628,...}, {1, 3, 24, 285, 4242, 73206, 1403028,...},...

CROSSREFS

Rows include A000007, A000108, A005568, A064037. Columns include A000012, A001477, A049450, A064046. Cf. A064044.

Sequence in context: A120568 A189233 A065066 * A110314 A152882 A130167

Adjacent sequences:  A064042 A064043 A064044 * A064046 A064047 A064048

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Aug 23 2001

STATUS

approved

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Last modified April 20 16:29 EDT 2014. Contains 240807 sequences.