Bruce Boghosian has authored 2 sequences.
A156744
Coefficients for estimation of derivative from equally spaced numerical data using the Lagrange interpolating polynomial.
Original entry on oeis.org
-1, 0, 1, 1, -8, 0, 8, -1, -1, 9, -45, 0, 45, -9, 1, 3, -32, 168, -672, 0, 672, -168, 32, -3
Offset: 1
Irregular triangle begins:
-1, 0, 1;
1, -8, 0, 8, -1;
-1, 9, -45, 0, 45, -9, 1;
3, -32, 168, -672, 0, 672, -168, 32, -3;
-2, 25, -150, 600, -2100, 0, 2100, -600, 150, -25, 2; ...
When divided by sequence
A099996, this triangle gives the coefficients needed to estimate derivatives from equally spaced numerical data using Lagrange interpolation. The first and last entry of each row of the triangle has absolute value lcm{1, 2, ..., 2*n}/n*binomial(2n, n), as seen in
A068553.
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facs[x_, j_, n_] := Product[If[k == j, 1, x - k], {k, -n, n}]
coefs[x_, n_] := Table[facs[x, j, n]/facs[j, j, n], {j, -n, n}]
d[n_] := Apply[LCM, Table[j, {j, 1, 2*n}]]
dCoefs[x_, n_] := d[n] D[coefs[y, n], y] /. {y -> x}
MatrixForm[Table[dCoefs[0, n], {n, 1, 5}]]
A112536
Natural numbers that can be factored into the product of three positive integers whose minimal sum is achieved in more than one way.
Original entry on oeis.org
360, 1008, 3696, 3960, 5040, 5850, 6240, 6552, 7425, 10800, 12285, 13464, 13600, 14280, 14688, 15120, 15300, 19008, 19152, 19800, 19950, 20064, 20520, 20790, 21280, 21600, 22491, 26775, 30240, 30800, 31050, 31200, 32760, 33696, 34398
Offset: 1
6552 = 14*18*26 = 13*21*24. Each triples' factors sum to 58 (14+18+26 = 58 and 13+21+24 = 58). 58 works out to be the minimal sum for all 3-factorizations of 6552 and there are two of them.
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