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 A099020 Euler-Seidel matrix T(k,n) with start sequence A001147, read by antidiagonals. 4
 1, 1, 0, 2, 1, 1, 4, 2, 1, 0, 10, 6, 4, 3, 3, 26, 16, 10, 6, 3, 0, 76, 50, 34, 24, 18, 15, 15, 232, 156, 106, 72, 48, 30, 15, 0, 764, 532, 376, 270, 198, 150, 120, 105, 105, 2620, 1856, 1324, 948, 678, 480, 330, 210, 105, 0, 9496, 6876, 5020, 3696, 2748, 2070, 1590, 1260, 1050, 945, 945 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS In an Euler-Seidel matrix, the rows are consecutive pairwise sums and the columns consecutive differences, with the first column the inverse binomial transform of the start sequence. LINKS Alois P. Heinz, Rows n = 0..140, flattened D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78. FORMULA Recurrence: T(0, 2n) = (2n-1)!!, T(0, 2n+1) = 0, T(k, n) = T(k-1, n) + T(k-1, n+1). EXAMPLE 1,   0,  1,  0,   3,   0,   15, ... 1,   1,  1,  3,   3,  15,   15, ... 2,   2,  4,  6,  18,  30,  120, ... 4,   6, 10, 24,  48, 150,  330, ... 10, 16, 34, 72, 198, 480, 1590, ... MAPLE T:= proc(k, n) option remember; `if`(k=0, `if`(irem(n, 2)=0,       doublefactorial(n-1), 0), T(k-1, n) +T(k-1, n+1))     end: seq(seq(T(d-n, n), n=0..d), d=0..14);  # Alois P. Heinz, Oct 14 2012 MATHEMATICA t[0, n_?EvenQ] := (n-1)!!; t[0, n_?OddQ] := 0; t[k_, n_] := t[k, n] = t[k-1, n] + t[k-1, n+1]; Table[t[k-n, n], {k, 0, 10}, {n, 0, k}] // Flatten (* Jean-François Alcover, Dec 10 2012 *) CROSSREFS First column is A000085, main diagonal is in A099021. Sequence in context: A021477 A124939 A187800 * A179438 A211970 A089688 Adjacent sequences:  A099017 A099018 A099019 * A099021 A099022 A099023 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Sep 23 2004 STATUS approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)