A302595 Triangle read by rows: T(n,k) is the number of ways to choose a k-dimensional subspace U of an n-dimensional vector space over GL(2) and then choose a subspace of U.

1, 2, 1, 5, 6, 1, 16, 35, 14, 1, 67, 240, 175, 30, 1, 374, 2077, 2480, 775, 62, 1, 2825, 23562, 43617, 22320, 3255, 126, 1, 29212, 358775, 997458, 791337, 188976, 13335, 254, 1, 417199, 7449060, 30495875, 36335970, 13452729, 1554480, 53975, 510, 1, 8283458, 213188689, 1268823220, 2226198875, 1237845378, 221753049, 12608560, 217175, 1022, 1, 229755605, 8473977534, 72697342949, 185429450580, 151826763275, 40848897474, 3600847129, 101563440, 871255, 2046, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k)/A005329(n) is the coefficient of y^k*x^n in (eq(x))^2*eq(y*x) where eq(x) is the q-exponential function.

Example

     1;
     2,     1;
     5,     6,     1;
    16,    35,    14,     1;
    67,   240,   175,    30,     1;
   374,  2077,  2480,   775,    62,     1;
  2825, 23562, 43617, 22320,  3255,   126,     1;

Mathematica

nn = 6; qq := 2; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}]; Map[Select[#, # > 0 &] &, Table[FunctionExpand[QFactorial[n, q]] /. q -> qq, {n, 0, nn}] CoefficientList[Series[eq[z]^2 eq[u z] /. q -> qq, {z, 0, nn}], {z, u}]] // Grid

Crossrefs

Sequence in context: A328297 A124575 A178121 * A113345 A078123 A342968

Adjacent sequences: A302592 A302593 A302594 * A302596 A302597 A302598

Keyword

nonn,tabl

Author

Geoffrey Critzer, Apr 10 2018

Status

approved