|
%I #7 Dec 26 2023 12:30:58
%S 2,1,1,1,6,1,1,37,37,1,1,226,606,226,1,1,1565,7972,7972,1565,1,1,
%T 13514,102407,187824,102407,13514,1,1,150753,1445555,3859373,3859373,
%U 1445555,150753,1,1,2105142,23789060,79955452,115641606,79955452,23789060
%N A symmetrical recursion triangular sequence: m=4; e(n,k,m)= (2* k + m - 1)e(n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m); t(n,k)=e(n, k, m) + e(n, n - k, m).
%C Row sums are:
%C {2, 2, 8, 76, 1060, 19076, 419668, 10911364, 327340916, 11129591140, 422924463316,...}.
%C Since m=2 is A060187, this recursion seems to be a MacMahon numbers level recursion.
%F m=4;e(n,k,m)= (2*k + m - 1)e)n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m);
%F t(n,k)=e(n, k, m) + e(n, n - k, m).
%e {2},
%e {1, 1},
%e {1, 6, 1},
%e {1, 37, 37, 1},
%e {1, 226, 606, 226, 1},
%e {1, 1565, 7972, 7972, 1565, 1},
%e {1, 13514, 102407, 187824, 102407, 13514, 1},
%e {1, 150753, 1445555, 3859373, 3859373, 1445555, 150753, 1},
%e {1, 2105142, 23789060, 79955452, 115641606, 79955452, 23789060, 2105142, 1},
%e {1, 34850041, 457127618, 1813119912, 3259697998, 3259697998, 1813119912, 457127618, 34850041, 1},
%e {1, 656682190, 9977604269, 46096675274, 96031672538, 117399194772, 96031672538, 46096675274, 9977604269, 656682190, 1}
%t Clear[e, n, k, m]; m = 4; e[n_, 0, m_] := 1;
%t e[n_, k_, m_] := 0 /; k >= n; e[n_, k_, 1] := 1 /; k >= n;
%t e[n_, k_, m_] := (2*k + m - 1)e[n - 1, k, m] + (m*n - 2*k + 1 - m)e[n - 1, k - 1, m];
%t Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}];
%t Flatten[%];
%t Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A060187.
%K nonn,tabl
%O 0,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Feb 06 2009
|
