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A099020 Euler-Seidel matrix T(k,n) with start sequence A001147, read by antidiagonals. 5
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
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, 2nd A013989, main diagonal is in A099021.
Sequence in context: A323873 A365582 A367559 * A179438 A211970 A089688
KEYWORD
nonn,tabl
AUTHOR
Ralf Stephan, Sep 23 2004
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)