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A108947
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Triangle: T(n,k) is the partition function G(n-k,k).
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1
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1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 4, 2, 1, 1, 0, 1, 10, 5, 2, 1, 1, 0, 1, 26, 14, 5, 2, 1, 1, 0, 1, 76, 46, 15, 5, 2, 1, 1, 0, 1, 232, 166, 51, 15, 5, 2, 1, 1, 0, 1, 764, 652, 196, 52, 15, 5, 2, 1, 1, 0, 1, 2620, 2780, 827, 202, 52, 15, 5, 2, 1, 1
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OFFSET
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0,13
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COMMENTS
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LINKS
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FORMULA
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E.g.f. for sequence G(0, k), G(1, k), ... is exp(x + (1/2)*x^2 + ... + (1/k!)*x^k).
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MAPLE
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G:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(G(n-i*j, i-1)*n!/i!^j/(n-i*j)!/j!, j=0..n/i)))
end:
T:= (n, k)-> G(n-k, k):
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MATHEMATICA
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G[n_, i_] := G[n, i] = If[n == 0, 1, If[i<1, 0, Sum[G[n-i*j, i-1]*n!/i!^j/(n-i*j)! /j!, {j, 0, n/i}]]]; T[n_, k_] := G[n-k, k]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)
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CROSSREFS
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Cf. A000110. First differences of a sequence G(k, 0), G(k, 1), ... give a row of A080510 (e.g., 0, 1, 10, 14, 15, 15, ... gives 1, 9, 4, 1).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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