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
KEYWORD
AUTHOR
David W. Wilson, Jan 12 2001
STATUS
approved