login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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