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Search: id:A157744
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| A157744 |
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A recursion triangle sequence: e(n,k)=Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}]; A(n,k)=A(n-1,k-1)+e(n-1,k). |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 6, 4, 1, 1, 2, 13, 17, 5, 1, 1, 2, 28, 79, 43, 6, 1, 1, 2, 59, 330, 381, 100, 7, 1, 1, 2, 122, 1250, 2746, 1572, 220, 8, 1, 1, 2, 249, 4415, 16869, 18365, 5865, 467, 9, 1, 1, 2, 504, 14857, 92649, 173059, 106599, 20473, 969, 10, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:
{1, 3, 6, 13, 38, 159, 880, 5921, 46242, 409123,...}.
The result is a nearly binomial experiment.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 470, Equation (38).
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FORMULA
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e(n,k)=Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}];
A(n,k)=A(n-1,k-1)+e(n-1,k).
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 2, 3, 1},
{1, 2, 6, 4, 1},
{1, 2, 13, 17, 5, 1},
{1, 2, 28, 79, 43, 6, 1},
{1, 2, 59, 330, 381, 100, 7, 1},
{1, 2, 122, 1250, 2746, 1572, 220, 8, 1},
{1, 2, 249, 4415, 16869, 18365, 5865, 467, 9, 1},
{1, 2, 504, 14857, 92649, 173059, 106599, 20473, 969, 10, 1}
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MATHEMATICA
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Clear[e, A, n, k];
e[n_, k_] := Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}];
A[1, n_] := 1;
A[n_, n_] := 1;
A[n_, k_] := A[n - 1, k - 1] + e[n - 1, k];
Table[Table[A[n, k], {k, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A117935 A103462 A116855 this_sequence A030111 A096921 A037161
Adjacent sequences: A157741 A157742 A157743 this_sequence A157745 A157746 A157747
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 05 2009
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