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A064044
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Square array read by antidiagonals of number of length k walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part.
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3
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 3, 6, 3, 1, 0, 6, 18, 12, 4, 1, 0, 10, 60, 51, 20, 5, 1, 0, 20, 200, 234, 108, 30, 6, 1, 0, 35, 700, 1110, 624, 195, 42, 7, 1, 0, 70, 2450, 5460, 3760, 1350, 318, 56, 8, 1, 0, 126, 8820, 27405, 23480, 9770, 2556, 483, 72, 9, 1, 0, 252
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| E.g.f. of row n equals ( besseli(0,2*y) + y*besseli(1,2*y) )^n. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2005
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
| a(n, k) = sum{j = 0, ..., k}[C(k, j)B(j)a(n-1, k-j)] where B(j) = C(j, [j/2]) = A001405(j) with a(0, 0) = 1
E.g.f: 1/(1 - x*besseli(0, 2*y) - x*y*besseli(1, 2*y)). - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2005
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EXAMPLE
| Rows start: {1, 0, 0, 0, 0,...}, {1, 1, 2, 3, 6,...}, {1, 2, 6, 18, 60,...}, {1, 3, 12, 51, 234,...},...
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PROG
| (PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); k!*polcoeff(polcoeff(1/(1-X*besseli(0, 2*Y)-X*Y*besseli(1, 2*Y)), n, x), k, y)} (Hanna)
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CROSSREFS
| Rows include A000007, A001405, A005566, A064036. Columns include A000012, A001477, A002378, A064043. Cf. A064045.
Sequence in context: A155161 A185937 A065177 * A144912 A145337 A171941
Adjacent sequences: A064041 A064042 A064043 * A064045 A064046 A064047
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001
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