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 A110135 Square array of expansions of 1/sqrt(1-4x-4*k*x^2), read by anti-diagonals. 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}; as a 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 A179863 A069123 Adjacent sequences:  A110132 A110133 A110134 * A110136 A110137 A110138 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Jul 13 2005 STATUS approved

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