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A137153
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Triangle, read by rows, where T(n,k) = C(2^k + n-k-1, n-k).
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4
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1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 8, 1, 1, 5, 20, 36, 16, 1, 1, 6, 35, 120, 136, 32, 1, 1, 7, 56, 330, 816, 528, 64, 1, 1, 8, 84, 792, 3876, 5984, 2080, 128, 1, 1, 9, 120, 1716, 15504, 52360, 45760, 8256, 256, 1, 1, 10, 165, 3432, 54264, 376992, 766480, 357760, 32896
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 4, 1;
1, 4, 10, 8, 1;
1, 5, 20, 36, 16, 1;
1, 6, 35, 120, 136, 32, 1;
1, 7, 56, 330, 816, 528, 64, 1;
1, 8, 84, 792, 3876, 5984, 2080, 128, 1;
1, 9, 120, 1716, 15504, 52360, 45760, 8256, 256, 1;
1, 10, 165, 3432, 54264, 376992, 766480, 357760, 32896, 512, 1; ...
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MATHEMATICA
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Table[Binomial[2^k+n-k-1, n-k], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 06 2017 *)
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PROG
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(PARI) {T(n, k)=binomial(2^k+n-k-1, n-k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
(PARI) {T(n, k) = polcoeff(1/(1-x+x*O(x^n))^(2^k), n-k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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