0,5

Also number of distinct binary linear [n,k] codes.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

D. Slepian, A class of binary signaling alphabets. Bell System Tech. J. 35 (1956), 203-234.

D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.

J. A. de Azcarraga and J. A. Macfarlane, Group Theoretical Foundations of Fractional Supersymmetry ,- Arxiv preprint hep-th/9506177, 1995 - arxiv.org: http://arxiv.org/abs/hep-th/9506177 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009]

T. D. Noe, Rows n=0..50 of triangle, flattened

Index entries for sequences related to binary linear codes

Weisstein, Eric W. q-Binomial Coefficient from Mathworld. [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Dec 05 2009]

G.f.: A(x,y) = Sum_{k>=0} y^k/Product_{j=0..k} (1 - 2^j*x). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009: (Start)

Definition of m here is q-1:

t(n,m)=If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

C(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])] (End)

Triangle begins:

1;

1, 1;

1, 3, 1;

1, 7, 7, 1;

1, 15, 35, 15, 1;

1, 31, 155, 155, 31, 1;

1, 63, 651, 1395, 651, 63, 1;

1, 127, 2667, 11811, 11811, 2667, 127, 1;

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009: (Start)

Clear[t, n, m, i, k, a, b];

t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

c = Table[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];

TableForm[c];

(*A022166, A022167, A022168, A022169, A022170, A022171, A022175*)

Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] (End)

(PARI) T(n, k)=polcoeff(x^k/prod(j=0, k, 1-2^j*x+x*O(x^n)), n) - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006

Contribution from Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Dec 05 2009: (Start)

(PARI) s = 9; q = 2; qp = matpascal(s, q);

for(n=1, s+1, for(k=1, n, print1(qp[n, k], ", ")) (End)

Row sums give A006116. Cf. A006516, A022167.

Central terms are A006098.

A022166, A022167, A022168, A022169, A022170, A022171, A022175 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009]

Sequence in context: A157152 A136126 A046802 this_sequence A141689 A058669 A057004

Adjacent sequences: A022163 A022164 A022165 this_sequence A022167 A022168 A022169

nonn,tabl,new

N. J. A. Sloane (njas(AT)research.att.com).