A141542 - OEIS

%I #4 Oct 12 2012 14:54:51

%S 1,1,1,1,2,1,1,3,3,1,1,12,18,12,1,1,10,60,60,10,1,1,11,55,220,55,11,1,

%T 1,13,74,245,245,74,13,1,1,16,104,383,319,383,104,16,1,1,17,135,603,

%U 553,553,603,135,17,1,1,19,167,869,967,1064,967,869,167,19,1

%N A triangular sequence of coefficients in a renormalized fractional factorial recursion ( a neo -combinatorial process): a(n) =a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4); Renormalized factorial; f(n) = a(n)*n*f(n - 1)/a(n - 1); Neo-combination: t(n, m) = f(n)/(f(n - m)*f(m)).

%C Row sum:

%C {1, 2, 4, 8, 44, 142, 354, 666, 1327, 2618, 5110}.

%F a(n) =a(n - 1) + a(n - 2) + a(n - 3) + a(n - 4); Renormalized factorial; f(n) = a(n)*n*f(n - 1)/a(n - 1); Neo-combination: t(n, m) = f(n)/(f(n - m)*f(m))

%e {1},

%e {1, 1},

%e {1, 2, 1},

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

%e {1, 12, 18, 12, 1},

%e {1, 10, 60, 60, 10, 1},

%e {1, 11, 55, 220, 55, 11, 1},

%e {1, 13, 74, 245, 245, 74, 13, 1},

%e {1, 16, 104, 383, 319, 383, 104, 16, 1},

%e {1, 17, 135, 603, 553, 553, 603, 135, 17, 1},

%e {1, 19, 167, 869, 967, 1064, 967, 869, 167, 19, 1}

%t Clear[a, n, f, g] a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4]; Table[a[n], {n, 0, 30}]; (* renormalized fractional factorial recursion*) f[0] = 1; f[1] = 1; f[n_] := f[n] = a[n]*n*f[n - 1]/a[n - 1]; Table[f[n], {n, 0, 10}]; g[n_, m_] := g[n, m] = f[n]/(f[n - m]*f[m]); Table[Table[Round[g[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[%]

%K nonn,uned,tabl

%O 1,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 16 2008