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A141542 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)). 0
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, 1, 13, 74, 245, 245, 74, 13, 1, 1, 16, 104, 383, 319, 383, 104, 16, 1, 1, 17, 135, 603, 553, 553, 603, 135, 17, 1, 1, 19, 167, 869, 967, 1064, 967, 869, 167, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sum:

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

LINKS

Table of n, a(n) for n=1..66.

FORMULA

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))

EXAMPLE

{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},

{1, 13, 74, 245, 245, 74, 13, 1},

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

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

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

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A171246 A129439 A176469 * A129453 A129455 A067924

Adjacent sequences:  A141539 A141540 A141541 * A141543 A141544 A141545

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Aug 16 2008

STATUS

approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)