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A105937 Infinite square array read by antidiagonals: T(m, 0) = 1, T(m, 1) = m; T(m, k) = (m - k + 1) T(m+1, k-1) - (k-1) (m+1) T(m+2, k-2). 9
1, 1, 0, 1, 1, -2, 1, 2, -2, 0, 1, 3, 0, -12, 36, 1, 4, 4, -24, 24, 0, 1, 5, 10, -30, -60, 420, -1800, 1, 6, 18, -24, -216, 720, -720, 0, 1, 7, 28, 0, -420, 420, 5040, -30240, 176400, 1, 8, 40, 48, -624, -960, 14400, -40320, 40320, 0, 1, 9, 54, 126, -756, -3780, 22680, 22680, -589680, 3764880, -28576800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

LINKS

G. C. Greubel, Antidiagonals n = 0..100, flattened

FORMULA

See A127080 for e.g.f.

EXAMPLE

Array begins

   1  1  1   1   1   1   1   1   1   1 ... (A000012)

   0  1  2   3   4   5   6   7   8   9 ... (A001477)

  -2 -2  0   4  10  18  28  40  54  70 ... (A028552)

   0 12 24  30  24   0  48 126 240 396 ... (A126935)

  36 24 60 216 420 624 756 720 396 360 ... (A126958)

...

MAPLE

T:= proc(n, k) option remember;

      if k=0 then 1

    elif k=1 then n

    else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)

      fi; end:

seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Jan 28 2020

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==1, n, (n-k+1)*T[n+1, k-1] - (k-1)*(n+1)* T[n+2, k-2]]]; Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 28 2020 *)

PROG

(PARI) T(n, k) = if(k==0, 1, if(k==1, n, (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2) )); \\ G. C. Greubel, Jan 28 2020

(MAGMA)

function T(n, k)

  if k eq 0 then return 1;

  elif k eq 1 then return n;

  else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);

  end if; return T; end function;

[T(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 28 2020

(Sage)

@CachedFunction

def T(n, k):

    if (k==0): return 1

    elif (k==1): return n

    else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)

[[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 28 2020

CROSSREFS

Rows give A000027, A028552, A126935, A126958.

Columns give A126934, A126962, A127067, A127068, A127070.

A127080 gives another version of the array.

Sequence in context: A122864 A140084 A243747 * A035146 A035216 A258587

Adjacent sequences:  A105934 A105935 A105936 * A105938 A105939 A105940

KEYWORD

sign,tabl

AUTHOR

Vincent v.d. Noort, Mar 24 2007

EXTENSIONS

More terms added by G. C. Greubel, Jan 28 2020

STATUS

approved

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Last modified November 30 11:07 EST 2021. Contains 349419 sequences. (Running on oeis4.)