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 A059268 Concatenate subsequences [2^0, 2^1, ..., 2^n] for n = 0, 1, 2, ... 24
 1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 32, 1, 2, 4, 8, 16, 32, 64, 1, 2, 4, 8, 16, 32, 64, 128, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Triangular array T(n,k) read by rows, where T(n,k) = i!*j! times coefficient of x^n*y^k in exp(x+2y). a(n) = A018900(n+1) - A140513(n). - Reinhard Zumkeller, Jun 24 2009 T(n,k) = A173786(n-1,k-1) - A173787(n-1,k-1), 0=1. - Boris Putievskiy, Dec 17 2012 As a linear array, the sequence is a(n) = 2^((n-1-t(t+1)/2), where t = floor(sqrt(2*n)-1/2), n>=1. - Zhining Yang, Jun 09 2017 EXAMPLE T(4,3)=8 since there are 8 subsets of {0,1,2,3,4} whose largest element is 3, namely, {3}, {0,3}, {1,3}, {2,3}, {0,1,3}, {0,2,3}, {1,2,3}, and {0,1,2,3}. Triangle starts: 1; 1, 2; 1, 2, 4; 1, 2, 4, 8; 1, 2, 4, 8, 16; 1, 2, 4, 8, 16, 32; ... MAPLE seq(seq(2^k, k=0..n), n=0..10); MATHEMATICA Table[2^k, {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 10 2013 *) PROG (Haskell) a059268 n k = a059268_tabl !! n !! k a059268_row n = a059268_tabl !! n a059268_tabl = iterate (scanl (+) 1) [1] -- Reinhard Zumkeller, Apr 18 2013, Jul 05 2012 CROSSREFS Cf. A140531. Cf. A000079. Cf. A131816. Row sums give A126646. Sequence in context: A059250 A303696 A131074 * A300653 A256009 A123937 Adjacent sequences: A059265 A059266 A059267 * A059269 A059270 A059271 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 23 2001 EXTENSIONS Formula corrected by Reinhard Zumkeller, Feb 23 2010 STATUS approved

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Last modified June 25 16:46 EDT 2024. Contains 373705 sequences. (Running on oeis4.)