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A110135 Square array of expansions of 1/sqrt(1-4x-4*k*x^2), read by antidiagonals. 2
1, 2, 1, 6, 2, 1, 20, 8, 2, 1, 70, 32, 10, 2, 1, 252, 136, 44, 12, 2, 1, 924, 592, 214, 56, 14, 2, 1, 3432, 2624, 1052, 304, 68, 16, 2, 1, 12870, 11776, 5284, 1632, 406, 80, 18, 2, 1, 48620, 53344, 26840, 9024, 2332, 520, 92, 20, 2, 1, 184756, 243392, 137638, 50304 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Column k has g.f. 1/sqrt(1-4x-4*k*x^2) and e.g.f. exp(2x)BesselI(0,2*sqrt(k)x). Columns include A000984, A006139, A084609, A098453. Row sums of triangle are A110136. Diagonal sums of triangle are A110137.
LINKS
FORMULA
Square array T(n, k) = Sum_{j=0..floor(n/2)} C(n, j)*C(2(n-j), n)*k^j.
Number triangle T1(n, k) = Sum_{j=0..floor((n-k)/2)} C(n-k, j)*C(2(n-k-j), n-k)*k^j;
EXAMPLE
As a square array, rows start
1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, ...
6, 8, 10, 12, 14, 16, ...
20, 32, 44, 56, 68, 80, ...
70, 136, 214, 304, 406, 520, ...
252, 592, 1052, 1632, 2332, 3152, ...
As a number triangle, rows start
1;
2, 1;
6, 2, 1;
20, 8, 2, 1;
70, 30, 10, 2, 1;
252, 136, 44, 12, 2, 1;
CROSSREFS
Sequence in context: A124730 A114283 A106187 * A114423 A335109 A179863
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jul 13 2005
STATUS
approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)