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A118352
Semi-diagonal (one row below central terms) of pendular triangle A118350 and equal to the self-convolution of the central terms (A118351).
5
1, 2, 13, 96, 770, 6530, 57612, 523446, 4864795, 46032288, 441981816, 4295393886, 42172388820, 417668676206, 4167719552099, 41861139949200, 422890327921650, 4294027462637528, 43801007565527184, 448625344231794792
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-2], {n, 2, 30}] (* G. C. Greubel, Feb 18 2021 *)
PROG
(PARI) {a(n)=polcoeff((serreverse(x*(1-3*x+sqrt((1-3*x)*(1-7*x)+x*O(x^n)))/2/(1-3*x))/x)^2, n)}
(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-2) for n in (2..30)] # G. C. Greubel, Feb 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 26 2006
STATUS
approved