

A133332


Triangle read by rows giving coefficients in expansion of (1+x+x^2+...+x^(n2))^n in powers of x.


1



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
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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 752758.


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..n2)^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 * A179680 A123562 A046218
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



