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A055815
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a(n) = T(2*n+3,n), array T as in A055807.
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7
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1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032
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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+3)*hypergeom([-n-2, n], [2], -1) = Sum_{s=1..n+3} binomial(n+3,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+3, 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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