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 A062111 Upper-right triangle resulting from binomial transform calculation for nonnegative integers. 10
 0, 1, 1, 4, 3, 2, 12, 8, 5, 3, 32, 20, 12, 7, 4, 80, 48, 28, 16, 9, 5, 192, 112, 64, 36, 20, 11, 6, 448, 256, 144, 80, 44, 24, 13, 7, 1024, 576, 320, 176, 96, 52, 28, 15, 8, 2304, 1280, 704, 384, 208, 112, 60, 32, 17, 9, 5120, 2816, 1536, 832, 448, 240, 128, 68, 36, 19, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS From Philippe Deléham, Apr 15 2007 (Start) This triangle can be found in the Laisant reference in the following form: ...............................5...11 ..........................4...9...20 .....................3...7..16...36 ................2...5..12..28..... ...........1...3...8..20..48..... ......0...1...4..12..32..80...... (End) Triangle A152920 reversed . [Philippe Deléham, Apr 21 2009] LINKS F. Ellermann, Illustration of binomial transforms C.-A. Laisant, Sur les tableaux de sommes - Nouvelles applications, Compt. Rendus de l'Association Francaise pour l'Avancement des Sciences, Aout. 04, 1893, pp. 206-216 (table given on p. 212). FORMULA a(n, n) = n; a(n, k)=a(n, k-1)+a(n+1, k) if k>n. a(n, k)=(k+n)*2^(k-n-1) if k >= n. T(2n,n) = 3*n*2^(n-1) = 3*A001787(n). [Philippe Deléham, Apr 21 2009] EXAMPLE Rows start (0,1,4,12,32,...), (1,3,8,20,...), (2,5,12,...), (3,7,...), etc. CROSSREFS Rows include (essentially) A001787, A001792, A045623, A045891, A034007. Diagonals include (essentially) A001477, A005408, A008586, A017113, A017113, A008598. Column sums are A058877. Cf. A111297, A159694, A159695, A159696, A159697. [Philippe Deléham, Apr 21 2009] Sequence in context: A227182 A065367 A033882 * A181596 A182142 A033881 Adjacent sequences:  A062108 A062109 A062110 * A062112 A062113 A062114 KEYWORD nonn,tabl AUTHOR Henry Bottomley, May 30 2001 STATUS approved

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Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)