A157744 - OEIS

%I #7 Aug 23 2022 09:44:49

%S 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,

%T 330,381,100,7,1,1,2,122,1250,2746,1572,220,8,1,1,2,249,4415,16869,

%U 18365,5865,467,9,1,1,2,504,14857,92649,173059,106599,20473,969,10,1

%N 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}].

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 470, Equation (38).

%F 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}].

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 2, 3, 1},

%e {1, 2, 6, 4, 1},

%e {1, 2, 13, 17, 5, 1},

%e {1, 2, 28, 79, 43, 6, 1},

%e {1, 2, 59, 330, 381, 100, 7, 1},

%e {1, 2, 122, 1250, 2746, 1572, 220, 8, 1},

%e {1, 2, 249, 4415, 16869, 18365, 5865, 467, 9, 1},

%e {1, 2, 504, 14857, 92649, 173059, 106599, 20473, 969, 10, 1}

%t Clear[e, A, n, k];

%t e[n_, k_] := Sum[(-1)^j Binomial[n + 1, j](k - j)^n, {j, 0, k}];

%t A[1, n_] := 1;

%t A[n_, n_] := 1;

%t A[n_, k_] := A[n - 1, k - 1] + e[n - 1, k];

%t Table[Table[A[n, k], {k, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Mar 05 2009