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A118353
Semi-diagonal (two rows below central terms) of pendular triangle A118350 and equal to the self-convolution cube of the central terms (A118351).
5
1, 3, 21, 163, 1353, 11760, 105681, 973953, 9154821, 87428388, 845894700, 8273978100, 81682757317, 812829371205, 8144563709391, 82104333340467, 832125695906313, 8473862660311392, 86661931504395228, 889705959333345756
OFFSET
0,2
LINKS
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==n, 0, T[n-1, k] - 3*T[n-1, k-1] + 3*T[n, k-1] + T[n+1, k-1] ]];
Table[T[n, n-3], {n, 3, 30}] (* G. C. Greubel, Feb 18 2021 *)
PROG
(PARI) my(x='x+O('x^33)); Vec((serreverse(x*(1-3*x+sqrt((1-3*x)*(1-7*x)))/2/(1-3*x))/x)^3)
(Sage)
@CachedFunction
def T(n, k):
if (k<0 or n<k): return 0
elif (k==0): return 1
elif (k==n): return 0
else: return T(n-1, k) - 3*T(n-1, k-1) + 3*T(n, k-1) + T(n+1, k-1)
[T(n, n-3) for n in (3..30)] # G. C. Greubel, Feb 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 26 2006
STATUS
approved