cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A249755 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.

Original entry on oeis.org

1, 1, 3, 1, 7, 3, 1, 12, 10, 3, 1, 18, 22, 13, 3, 1, 25, 40, 35, 16, 3, 1, 33, 65, 75, 51, 19, 3, 1, 42, 98, 140, 126, 70, 22, 3, 1, 52, 140, 238, 266, 196, 92, 25, 3, 1, 63, 192, 378, 504, 462, 288, 117, 28, 3, 1, 75, 255, 570, 882, 966, 750, 405, 145, 31
Offset: 0

Views

Author

Clark Kimberling, Nov 07 2014

Keywords

Comments

(Sum of numbers in row n) = A000295(n+1) for n >= 0.

Examples

			p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 7*x + 3*x^2
First 6 rows:
1
1   3
1   7    3
1   12   10   3
1   18   22   13   3
1   25   40   35   16   3

Links

Crossrefs

Cf. A249756, A249757, A000295.

Programs

  • Mathematica
    z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)
Flatten[CoefficientList[t, x]] (* A249755 sequence *)

A249757 Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.

Original entry on oeis.org

1, 1, 3, 1, 8, 3, 1, 15, 11, 3, 1, 24, 26, 14, 3, 1, 35, 50, 40, 17, 3, 1, 48, 85, 90, 57, 20, 3, 1, 63, 133, 175, 147, 77, 23, 3, 1, 80, 196, 308, 322, 224, 100, 26, 3, 1, 99, 276, 504, 630, 546, 324, 126, 29, 3, 1, 120, 375, 780, 1134, 1176, 870, 450, 155
Offset: 0

Views

Author

Clark Kimberling, Nov 07 2014

Keywords

Comments

(Sum of numbers in row n) = A097809(n) for n >= 0.

Examples

			p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 8*x + 3*x^2
First 6 rows:
1
1   3
1   8    3
1   15   11    3
1   24   26    14   3
1   35   50    40   17   3

Links

Crossrefs

Cf. A249755, A249756, A097809.

Programs

  • Mathematica
    z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + 2*n*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249757 array *)
Flatten[CoefficientList[t, x]] (* A249757 sequence *)

A249758 Triangular array of coefficients of polynomials p(n,x) = (x + 2)*p(n-1,x) + x, p(0,x) = 1.

Original entry on oeis.org

1, 2, 2, 4, 7, 2, 8, 19, 11, 2, 16, 47, 41, 15, 2, 32, 111, 129, 71, 19, 2, 64, 255, 369, 271, 109, 23, 2, 128, 575, 993, 911, 489, 155, 27, 2, 256, 1279, 2561, 2815, 1889, 799, 209, 31, 2, 512, 2815, 6401, 8191, 6593, 3487, 1217, 271, 35, 2, 1024, 6143
Offset: 0

Views

Author

Clark Kimberling, Nov 07 2014

Keywords

Examples

			p(0,x) = 1
p(1,x) = 2 + 2*x
p(2,x) = 4 + 7*x + 2*x^2
First 6 rows:
1
2    2
4    7     2
8    19    11    2
16   47    41    15    2
32   111   129   71    19   2

Links

Crossrefs

Cf. A249755, A249756.

Programs

  • Mathematica
    z = 14; p[n_, x_] := (x + 2) p[n - 1, x] + x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249758 array *)
Flatten[CoefficientList[t, x]] (* A249758 sequence *)
Showing 1-3 of 3 results.

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