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A235803
Rectangular array read by upward antidiagonals: A(n,k) = 1 + sqrt(k)*((1+sqrt(k))^n - (1-sqrt(k))^n)/2, n,k >= 0.
0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 9, 11, 7, 5, 1, 1, 17, 25, 19, 9, 6, 1, 1, 33, 59, 49, 29, 11, 7, 1, 1, 65, 141, 133, 81, 41, 13, 8, 1, 1, 129, 339, 361, 245, 121, 55, 15, 9, 1, 1, 257, 817, 985, 729, 401, 169, 71, 17, 10, 1
OFFSET
0,5
FORMULA
A(0,k) = 1, A(n,k) = 1 + k*(sum_{j=0..floor((n-1)/2)} A034867(n,j)*k^j), n>0.
EXAMPLE
Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ...
1, 5, 11, 19, 29, 41, 55, 71, 89, 109, ...
1, 9, 25, 49, 81, 121, 169, 225, 289, 361, ...
1, 17, 59, 133, 245, 401, 607, 869, 1193, 1585, ...
1, 33, 141, 361, 729, 1281, 2053, 3081, 4401, 6049, ...
1, 65, 339, 985, 2189, 4161, 7135, 11369, 17145, 24769, ...
1, 129, 817, 2689, 6561, 13441, 24529, 41217, 65089, 97921, ...
1, 257, 1971, 7345, 19685, 43521, 84727, 150641, 250185, 393985, ...
As a triangle:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 5, 5, 4, 1;
1, 9, 11, 7, 5, 1;
1, 17, 25, 19, 9, 6, 1;
1, 33, 59, 49, 29, 11, 7, 1; ...
CROSSREFS
Cf. A094373 (column k=1)
Sequence in context: A174802 A238346 A053538 * A138201 A220614 A154221
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Jan 15 2014
STATUS
approved