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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.
1
-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
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
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Sep 13 2006
EXTENSIONS
Edited by G. C. Greubel, Jul 12 2021
STATUS
approved