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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. 18
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
LINKS
FORMULA
See program.
EXAMPLE
Triangle begins:
1;
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.
Diagonal and lower diagonals 1-3 give: A000012, A000217, A000914, A001303.
Row sums are in A052593.
Sequence in context: A145643 A338208 A323155 * A137738 A350624 A009108
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 03 2008
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)