A145142 - OEIS

A145142

Triangle T(n,k), n>=1, 0<=k<=n-1, read by rows: T(n,k)/(n-1)! is the coefficient of x^k in polynomial p_n for the n-th row sequence of A145153.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 24, 6, 11, 6, 1, 120, 144, 50, 35, 10, 1, 720, 1200, 634, 225, 85, 15, 1, 5040, 9960, 6804, 2464, 735, 175, 21, 1, 80640, 89040, 71868, 29932, 8449, 1960, 322, 28, 1, 1088640, 1231776, 789984, 375164, 112644, 25473, 4536, 546, 36, 1

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OFFSET

1,8

LINKS

Alois P. Heinz, Rows n = 1..45, flattened

FORMULA

See program.

EXAMPLE

Triangle begins:

0, 1;

0, 1, 1;

0, 2, 3, 1;

24, 6, 11, 6, 1;

120, 144, 50, 35, 10, 1;

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)-> `if`(k<0 or k>=n, 0, coeff(row(n)(x), x, k)*(n-1)!): seq(seq(T(n, k), k=0..n-1), n=1..12);

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]*(n-1)!, {n, 1, 12}] // Flatten (* Jean-François Alcover, Feb 04 2014, after Alois P. Heinz *)

CROSSREFS

T(n,k)/(n-1)! gives: A145140 / A145141.

Columns 0-9 give: A052581, A145143, A145144, A145145, A145146, A145147, A145148, A145149, A145150.

Diagonal and lower diagonals 1-3 give: A000012, A000217, A000914, A001303.

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

Row sums are in A052593.

Sequence in context: A145643 A338208 A323155 * A137738 A350624 A009108

Adjacent sequences: A145139 A145140 A145141 * A145143 A145144 A145145

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Oct 03 2008

STATUS

approved