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A157744
A recursion triangle sequence: A(n,k) = A(n-1,k-1)+e(n-1,k) where e(n,k)=Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}].
0
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
OFFSET
0,5
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 470, Equation (38).
FORMULA
A(n,k) = A(n-1,k-1)+e(n-1,k) where e(n,k) = Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}].
EXAMPLE
{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}
MATHEMATICA
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[%]
CROSSREFS
Sequence in context: A225641 A116855 A173265 * A335545 A334997 A030111
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved