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A145140 Numerators of triangle T(n,k), n>=1, 0<=k<=n - 1, read by rows: T(n,k) is the coefficient of x^k in polynomial p_n for the n-th row sequence of A145153. 9
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 11, 1, 1, 1, 6, 5, 7, 1, 1, 1, 5, 317, 5, 17, 1, 1, 1, 83, 27, 22, 7, 5, 1, 1, 2, 53, 5989, 1069, 1207, 7, 23, 1, 1, 3, 611, 2743, 93791, 149, 1213, 1, 13, 1, 1, 4, 101, 25523, 5419, 20071, 397, 3253, 1, 29, 1, 1, 5, 32419, 11017, 30731, 21757 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,13

LINKS

Table of n, a(n) for n=1..71.

FORMULA

See program.

EXAMPLE

1, 0, 1, 0, 1/2, 1/2, 0, 1/3, 1/2, 1/6, 1, 1/4, 11/24, 1/4, 1/24, 1, 6/5, 5/12, 7/24, 1/12, 1/120, 1, 5/3, 317/360, 5/16, 17/144, 1/48, 1/720 ... = A145140/A145141

As triangle:

  1

  0 1

  0 1/2 1/2

  0 1/3 1/2 1/6

  1 1/4 11/24 1/4 1/24

  1 6/5 5/12 7/24 1/12 1/120

MAPLE

row:= proc(n) option remember; local f, i, x; f:= unapply(simplify(sum('cat(a||i) *x^i', 'i'=0..n-1) ), x); unapply(subs(solve({seq(f(i+1)= coeftayl(x/ (1-x-x^4)/ (1-x)^i, x=0, n), i=0..n-1)}, {seq(cat(a||i), i=0..n-1)}), sum('cat(a||i) *x^i', 'i'=0..n-1) ), x); end: T:= (n, k)-> coeff(row(n)(x), x, k): seq(seq(numer(T(n, k)), k=0..n-1), n=1..14);

MATHEMATICA

row[n_] := Module[{f, eq}, f = Function[x, Sum[a[k]*x^k, {k, 0, n-1}]]; eq = Table[f[k+1] == SeriesCoefficient[x/(1-x-x^4)/(1-x)^k, {x, 0, n}], {k, 0, n-1}]; Table[a[k], {k, 0, n-1}] /. Solve[eq] // First]; Table[row[n] // Numerator, {n, 1, 14}] // Flatten (* Jean-François Alcover, Feb 04 2014, after Alois P. Heinz *)

CROSSREFS

Denominators of T(n, k): A145141. T(n, k)*(n-1)!: A145142.

Row sums give: A003269, A017898(n+3).

Cf. A145153, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130.

Sequence in context: A010194 A280443 A107045 * A010195 A010193 A214679

Adjacent sequences:  A145137 A145138 A145139 * A145141 A145142 A145143

KEYWORD

frac,nonn,tabl

AUTHOR

Alois P. Heinz, Oct 03 2008

STATUS

approved

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Last modified August 24 03:20 EDT 2019. Contains 326260 sequences. (Running on oeis4.)