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A027272
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Self-convolution of row n of array T given by A026552.
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18
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1, 3, 19, 58, 462, 1608, 13446, 48924, 417440, 1553940, 13409576, 50618184, 440013462, 1676640462, 14649846820, 56201554888, 492944907180, 1900789437276, 16721000706580, 64734185205960, 570792185166764, 2216888144737508, 19584623363041704, 76265067399850848
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OFFSET
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0,2
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LINKS
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FORMULA
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, 2*n-k], {k, 0, 2*n}]];
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+2)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n, k)*T(n, 2*n-k) for k in (0..2*n) )
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CROSSREFS
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Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027273, A027274, A027275, A027276.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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