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

%I

%S 1,1,3,3,1,1,4,10,16,19,16,10,4,1,1,5,15,35,65,101,135,155,155,135,

%T 101,65,35,15,5,1,1,6,21,56,126,246,426,666,951,1246,1506,1686,1751,

%U 1686,1506,1246,951,666,426,246,126,56,21,6,1,1,7,28,84,210,462,917

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

%H Harvey P. Dale, <a href="/A133332/b133332.txt">Table of n, a(n) for n = 2..1000</a>

%H Warren P. Johnson, <a href="http://www.jstor.org/stable/27642326">Mathematics and Social Utopias in France: Olinde Rodrigues and His times by Simon Altmann; Eduardo L. Ortiz</a>, American Math. Monthly, Oct 2007, volume 114, number 8, pages 752-758.

%e Triangle begins:

%e {1},

%e {1, 3, 3, 1},

%e {1, 4, 10, 16, 19, 16, 10, 4, 1},

%e {1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1},

%e {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},

%e ...

%p (Maple code from _N. J. A. Sloane_, Feb 15 2015):

%p U:=n->seriestolist(series(expand(add(x^i,i=0..n-2)^n),x,100000));

%p for n from 2 to 8 do lprint(U(n)); od:

%t 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}]

%t Flatten[Table[Drop[CoefficientList[Expand[Total[x^Range[n]]^(n+1)],x], n+1],{n,6}]] (* _Harvey P. Dale_, Feb 15 2015 *)

%K nonn,tabf

%O 2,3

%A _Roger L. Bagula_, Oct 19 2007

%E Edited by _N. J. A. Sloane_, Feb 15 2015

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)