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A055816
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a(n) = T(2*n+4,n), array T as in A055807.
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7
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1, 31, 192, 1120, 6400, 36288, 205184, 1159488, 6554880, 37088480, 210075712, 1191254688, 6762782208, 38434677120, 218663320320, 1245254943872, 7098135387648, 40495661150112, 231220652273600, 1321222104326880
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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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a(n) = (n+4)*hypergeom([-n -3, n], [2], -1) = Sum_{s=1..n+4} binomial(n+4,s)*binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021
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MAPLE
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T:= proc(i, j) option remember;
if j=0 then 1
elif i=0 then 0
else add(add(T(h, m), m=0..j), h=0..i-1)
fi; end:
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MATHEMATICA
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T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h, 0, i-1}, {m, 0, j}]]]; Table[T[n+4, n], {n, 0, 20}] (* G. C. Greubel, Jan 23 2020 *)
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PROG
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(Sage)
@CachedFunction
def T(i, j):
if (j==0): return 1
elif (i==0): return 0
else: return sum(sum(T(h, m) for m in (0..j)) for h in (0..i-1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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