A122053 Triangle T(n, k) = 2*(-1 + 2*k)*T(n-1, k) - T(n-2, k) with T(-2, k) = T(-1, k) = 1, read by rows.

-3, 5, 1, -7, 1, 169, 9, 1, 985, 8721, -11, 1, 5741, 86329, 489061, 13, 1, 33461, 854569, 6811741, 31622993, -15, 1, 195025, 8459361, 94875313, 567451585, 2351330961, 17, 1, 1136689, 83739041, 1321442641, 10182505537, 51622180721, 198710804449

Offset

0,1

References

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964, 9th Printing (1970), pp. 782.

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

T(n, k) = 2*(-1 + 2*k)*T(n-1, k) - T(n-2, k) with T(-2, k) = T(-1, k) = 1.

Example

Triangle begins as:
   -3;
    5, 1;
   -7, 1,    169;
    9, 1,    985,    8721;
  -11, 1,   5741,   86329,   489061;
   13, 1,  33461,  854569,  6811741,  31622993;
  -15, 1, 195025, 8459361, 94875313, 567451585, 2351330961;

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 1, 2*(-1+2*k)*T[n-1, k] - T[n-2, k]];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma)
function T(n, k)
  if n lt 0 then return 1;
  else return 2*(-1+2*k)*T(n-1, k) - T(n-2, k);
  end if; return T;
end function;
[T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 12 2021
(Sage)
def T(n, k): return 1 if (n<0) else 2*(-1 + 2*k)*T(n-1, k) - T(n-2, k)
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 12 2021

Crossrefs

Sequence in context: A346775 A028510 A338721 * A124084 A133045 A320051

Adjacent sequences: A122050 A122051 A122052 * A122054 A122055 A122056

Keyword

sign,tabl

Author

Roger L. Bagula, Sep 13 2006

Extensions

Edited by G. C. Greubel, Jul 12 2021

Status

approved