A108284 Triangle read by rows, related to A108283.

1, 3, 2, 6, 11, 6, 10, 39, 54, 24, 15, 114, 304, 324, 120, 21, 300, 1384, 2664, 2280, 720, 28, 741, 5598, 17364, 25800, 18360, 5040, 36, 1757, 21054, 99012, 227400, 273720, 166320, 40320, 45, 4052, 75504, 518592, 1728816, 3131400, 3160080, 1673280, 362880, 55, 9162, 262104, 2564892, 11934816, 30523800, 45496080, 39473280, 18506880, 3628800

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

n-th row is the inverse binomial transform of n-th column of A108283.

Example

Triangle begins:
1;
3, 2;
6, 11, 6;
10, 39, 54, 24;
15, 114, 304, 324, 120; ...
Row 2: (3, 2, 0, 0, 0...), is the inverse binomial transform of column 2 of A108283: (3, 5, 7, 9...).

Mathematica

(* T = A108283 *) T[_, 1] := 1; T[n_, n_] := n*(n + 1)/2; T[n_, k_] := (1 - (n - k + 1)^k*(k^2 - k*n + 1))/(n - k)^2; row[n_] := (TT = Table[T[k, n], {k, n, 2*n - 1}]; Table[Differences[TT, k], {k, 0, n - 1}][[All, 1]]); Table[row[n], {n, 1, 10}] // Flatten (* Jean-François Alcover, Sep 13 2016 *)

Crossrefs

Cf. A108283.

Sequence in context: A362373 A364929 A109876 * A340733 A095011 A274975

Adjacent sequences: A108281 A108282 A108283 * A108285 A108286 A108287

Keyword

nonn,tabl

Author

Gary W. Adamson, May 30 2005

Extensions

More terms from Jean-François Alcover, Sep 13 2016

Status

approved