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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 A323312

Adjacent sequences:  A302592 A302593 A302594 * A302596 A302597 A302598

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Apr 10 2018

STATUS

approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)