A058942 Triangle of coefficients of Gandhi polynomials.

1, 1, 1, 2, 4, 2, 8, 22, 20, 6, 56, 184, 224, 120, 24, 608, 2248, 3272, 2352, 840, 120, 9440, 38080, 62768, 54336, 26208, 6720, 720, 198272, 856480, 1550528, 1531344, 896064, 312480, 60480, 5040, 5410688, 24719488, 48207488, 52633344, 35371776

Offset

1,4

Comments

(1+x)^2 divides these polynomials for n > 2. - T. D. Noe, Jan 01 2008

Links

T. D. Noe, Rows n = 1..50 of triangle, flattened

Formula

C_1(x) = 1; C_n(x) = (x+1)*((x+1)*C_n-1(x+1) - x*C_n-1(x)).

Triangle T(n, k), read by rows; given by [1, 1, 4, 4, 9, 9, 16, 16, 25, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 24 2005

Example

Triangle starts:
[1]
[1,      1]
[2,      4,      2]
[8,      22,     20,      6]
[56,     184,    224,     120,     24]
[608,    2248,   3272,    2352,    840,    120]
[9440,   38080,  62768,   54336,   26208,  6720,   720]
[198272, 856480, 1550528, 1531344, 896064, 312480, 60480, 5040]

Mathematica

c[1][x_] = 1; c[n_][x_] :=  c[n][x] = (x+1)*((x+1)*c[n-1][x+1] - x*c[n-1][x]); Table[ CoefficientList[ c[n][x], x], {n, 9}] // Flatten (* Jean-François Alcover, Oct 09 2012 *)

Prog

(Sage) # uses[delehamdelta from A084938]
def A058942_triangle(n) :
    A = [((i+1)//2)^2 for i in (1..n)]
    B = [((i+1)//2) for i in (1..n)]
    return delehamdelta(A, B)
A058942_triangle(10) # Peter Luschny, Nov 09 2019

Crossrefs

First column is A005439, as are row sums. See also A036970.

Cf. A084938.

Sequence in context: A356257 A229296 A232565 * A365638 A196759 A303165

Adjacent sequences: A058939 A058940 A058941 * A058943 A058944 A058945

Keyword

nonn,tabl,nice

Author

David W. Wilson, Jan 12 2001

Status

approved