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A055818
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Triangle T read by rows: T(i,j) = R(i-j,j), where R(i,0) = R(0,i) = 1 for i >= 0, R(i,j) = Sum_{h=0..i-1} Sum_{m=0..j} R(h,m) for i >= 1, j >= 1.
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13
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1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 11, 9, 4, 1, 1, 23, 24, 14, 5, 1, 1, 47, 60, 43, 20, 6, 1, 1, 95, 144, 122, 69, 27, 7, 1, 1, 191, 336, 328, 217, 103, 35, 8, 1, 1, 383, 768, 848, 640, 354, 146, 44, 9, 1, 1, 767, 1728, 2128, 1800, 1131, 543, 199, 54, 10, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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EXAMPLE
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Rows begins as:
1;
1, 1;
1, 2, 1;
1, 5, 3, 1;
1, 11, 9, 4, 1;
...
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MAPLE
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T:= proc(i, j) option remember;
if i=0 or j=0 then 1
else add(add(T(h, m), m=0..j), h=0..i-1)
fi; end:
seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Jan 21 2020
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MATHEMATICA
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T[i_, j_]:= T[i, j]= If[i==0 || j==0, 1, Sum[T[h, m], {h, 0, i-1}, {m, 0, j}]]; Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 21 2020 *)
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PROG
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(PARI) T(i, j) = if(i==0 || j==0, 1, sum(h=0, i-1, sum(m=0, j, T(h, m) )));
for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Jan 21 2020
(Magma)
function T(i, j)
if i eq 0 or j eq 0 then return 1;
else return (&+[(&+[T(h, m): m in [0..j]]): h in [0..i-1]]);
end if; return T; end function;
[T(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 21 2020
(Sage)
@CachedFunction
def T(i, j):
if (i==0 or j==0): return 1
else: return sum(sum(T(h, m) for m in (0..j)) for h in (0..i-1))
[[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 21 2020
(GAP)
T:= function(i, j)
if i=0 or j=0 then return 1;
else return Sum([0..i-1], h-> Sum([0..j], m-> T(h, m) ));
fi; end;
Flat(List([0..12], n-> List([0..n], k-> T(n-k, k) ))); # G. C. Greubel, Jan 21 2020
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CROSSREFS
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Cf. A055819, A055820, A055821, A055822, A055823, A055824, A055825, A055826, A055827, A055828, A055829.
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KEYWORD
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AUTHOR
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STATUS
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approved
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