A136160 Triangle T(n,k) = k*A053120(n,k).
1, 0, 4, -3, 0, 12, 0, -16, 0, 32, 5, 0, -60, 0, 80, 0, 36, 0, -192, 0, 192, -7, 0, 168, 0, -560, 0, 448, 0, -64, 0, 640, 0, -1536, 0, 1024, 9, 0, -360, 0, 2160, 0, -4032, 0, 2304, 0, 100, 0, -1600, 0, 6720, 0, -10240, 0, 5120, -11, 0, 660, 0, -6160, 0, 19712, 0, -25344, 0, 11264
Offset: 1
Examples
1; 0, 4; -3, 0, 12; 0, -16, 0, 32; 5, 0, -60, 0, 80; 0, 36, 0, -192, 0, 192; -7, 0, 168, 0, -560, 0, 448; 0, -64, 0, 640, 0, -1536,0, 1024; 9, 0, -360, 0, 2160,0, -4032, 0, 2304; 0, 100, 0, -1600, 0, 6720, 0, -10240, 0, 5120; -11, 0, 660, 0, -6160, 0, 19712, 0, -25344, 0, 11264;
References
- Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 8 and pages 42 - 43
Links
- Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
Programs
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Mathematica
P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - P[x, n - 2]; Q[x_, n_] := D[P[x, n + 1], x]; a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a]
Comments