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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 Table of n, a(n) for n=0..58. 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 Adjacent sequences: A110132 A110133 A110134 * A110136 A110137 A110138 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.)