A133332 Triangle read by rows giving coefficients in expansion of (1+x+x^2+...+x^(n-2))^n in powers of x.

1, 1, 3, 3, 1, 1, 4, 10, 16, 19, 16, 10, 4, 1, 1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1, 1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506, 1246, 951, 666, 426, 246, 126, 56, 21, 6, 1, 1, 7, 28, 84, 210, 462, 917

Offset

2,3

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Warren P. Johnson, Mathematics and Social Utopias in France: Olinde Rodrigues and His times by Simon Altmann; Eduardo L. Ortiz, American Math. Monthly, Oct 2007, volume 114, number 8, pages 752-758.

Example

Triangle begins:
{1},
{1, 3, 3, 1},
{1, 4, 10, 16, 19, 16, 10, 4, 1},
{1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1},
{1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506,1246, 951, 666, 426, 246, 126, 56, 21, 6, 1},
...

Maple

(Maple code from N. J. A. Sloane, Feb 15 2015):
U:=n->seriestolist(series(expand(add(x^i, i=0..n-2)^n), x, 100000));
for n from 2 to 8 do lprint(U(n)); od:

Mathematica

f[q_, n_] = If[n == 0, 1, Sum[q^i, {i, 0, n - 1}]]; g[q_, n_] = Product[f[q, n], {m, 0, n}]; a = Table[CoefficientList[g[x, n], x], {n, 0, 10}]
Flatten[Table[Drop[CoefficientList[Expand[Total[x^Range[n]]^(n+1)], x], n+1], {n, 6}]] (* Harvey P. Dale, Feb 15 2015 *)

Crossrefs

Sequence in context: A296523 A171876 A306462 * A362895 A179680 A123562

Adjacent sequences: A133329 A133330 A133331 * A133333 A133334 A133335

Keyword

nonn,tabf

Author

Roger L. Bagula, Oct 19 2007

Extensions

Edited by N. J. A. Sloane, Feb 15 2015

Status

approved