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A129458
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Row sums of triangle A129065 (v=1 member of a family).
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3
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1, 1, 3, 23, 329, 7545, 253195, 11692735, 710944785, 55043460305, 5286546264275, 616743770648775, 85901526469924825, 14079397690024018825, 2682416268746051840475, 587823624532842773747375, 146813897212611204795118625, 41456888496977804292047054625
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OFFSET
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0,3
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COMMENTS
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See A129065 for the M. Bruschi et al. reference.
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LINKS
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FORMULA
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a(n) = (2*n^2 - 4*n + 3)*a(n-1) - (n-2)^2*(n-1)^2*a(n-2).
a(n) ~ c * n^(2*n+(sqrt(5)-1)/2) / exp(2*n), where c = 6.07482758856838398336112197806575192722726...
(End)
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n==0, 1, 2*(n-1)^2*T[n-1, k] - 4*Binomial[n-1, 2]^2*T[n-2, k] +T[n-1, k-1] ]]; (* T = A129065 *)
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PROG
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(SageMath)
@CachedFunction
if (k<0 or k>n): return 0
elif (n==0): return 1
else: return 2*(n-1)^2*T(n-1, k) - 4*binomial(n-1, 2)^2*T(n-2, k) + T(n-1, k-1)
def A129458(n): return sum(T(n, k) for k in range(n+1))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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