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 A209235 Rectangular array read by antidiagonals, with entry k in row n given by T(n,k) = 2^{k-1}*Sum_{j=1..n} (cos((2*j-1)*Pi/(2*n+1)))^{k-1}. 2
 1, 2, 1, 3, 1, 1, 4, 1, 3, 1, 5, 1, 5, 4, 1, 6, 1, 7, 4, 7, 1, 8, 1, 11, 4, 19, 16, 18, 1, 9, 1, 13, 4, 25, 16, 38, 29, 1, 10, 1, 15, 4, 31, 16, 58, 57, 47, 1, 11, 1, 17, 4, 37, 16, 78, 64, 117, 76, 1, 12, 1, 19, 4, 43, 16, 98, 64, 187, 193, 123, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS (Start) Array begins as .1..1...1..1...1...1 .2..1...3..4...7..11 .3..1...5..4..13..16 .4..1...7..4..19..16 .5..1...9..4..25..16 .6..1..11..4..31..16   (End) Antidiagonal sums: {1,3,5,9,16,26,46,78,136,...}. LINKS FORMULA T(n,k) = 2^{k-1}*Sum_{j=1..n} (cos((2*j-1)*Pi/(2*n+1)))^{k-1}. Empirical g.f. for row n: F(x) = (Sum_{u=0..n-1} A122765(n,n-1-u)*x^u)/(Sum_{v=0..n} A108299(n,v)*x^v). Empirical: odd column first differences tend to A000984 = {1, 2, 6, 20, 70, 252, ...} (central binomial coefficients). CROSSREFS Rows: cf. A000012, A000032, A094649, A189234, A216605, etc. Cf. A185095, A186740. Sequence in context: A178340 A173261 A084296 * A062534 A143349 A335123 Adjacent sequences:  A209232 A209233 A209234 * A209236 A209237 A209238 KEYWORD nonn,tabl AUTHOR L. Edson Jeffery, Jan 12 2013 STATUS approved

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Last modified August 10 08:28 EDT 2020. Contains 336368 sequences. (Running on oeis4.)