The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A249755

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.
(history; published version)

#8 by N. J. A. Sloane at Fri Nov 14 21:13:42 EST 2014

STATUS

editing

approved

#7 by N. J. A. Sloane at Fri Nov 14 21:13:40 EST 2014

CROSSREFS

Cf. A249756, A249757, A000295.

STATUS

approved

editing

#6 by N. J. A. Sloane at Fri Nov 14 21:11:29 EST 2014

STATUS

editing

approved

#5 by N. J. A. Sloane at Fri Nov 14 21:11:25 EST 2014

COMMENTS

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

STATUS

proposed

editing

#4 by Clark Kimberling at Fri Nov 14 09:09:15 EST 2014

STATUS

editing

proposed

#3 by Clark Kimberling at Fri Nov 07 18:09:08 EST 2014

NAME

allocated for Clark KimberlingTriangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.

DATA

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

0,3

COMMENTS

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

LINKS

Clark Kimberling, <a href="/A249755/b249755.txt">Rows n = 0..100, flattened</a>

EXAMPLE

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

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 *)

CROSSREFS

Cf. A249756, A249757.

KEYWORD

allocated

nonn,tabl,easy

AUTHOR

Clark Kimberling, Nov 07 2014

STATUS

approved

editing

#2 by Clark Kimberling at Tue Nov 04 20:58:25 EST 2014

KEYWORD

allocating

allocated

#1 by Clark Kimberling at Tue Nov 04 20:58:25 EST 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocating

STATUS

approved