A022166 -id:A022166 - cp's OEIS frontend

A157785 Triangle of coefficients of the polynomials defined by q^binomial(n, 2)*QPochhammer(x, 1/q, n), where q = -2.

1, 1, -1, -2, 1, 1, -8, 6, 3, -1, 64, -40, -30, 5, 1, 1024, -704, -440, 110, 11, -1, -32768, 21504, 14784, -3080, -462, 21, 1, -2097152, 1409024, 924672, -211904, -26488, 1806, 43, -1, 268435456, -178257920, -119767040, 26199040, 3602368, -204680, -7310, 85, 1

Offset: 0

Roger L. Bagula, Mar 06 2009

Triangle T(n,k), 0 <= k <= n, read by rows given by [1, q-1, q^2, q^3-q, q^4, q^5-q^2, q^6, q^7-q^3, q^8, ...] DELTA [-1, 0, -q, 0, -q^2, 0, -q^3, 0, -q^4, 0, ...] (for q=-2) = [1, -3, 4, -6, 16, -36, 64,...] DELTA [ -1, 0, 2, 0, -4, 0, 8, 0, -16, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 10 2009

			Triangle begins as:
          1;
          1,         -1;
         -2,          1,          1;
         -8,          6,          3,       -1;
         64,        -40,        -30,        5,       1;
       1024,       -704,       -440,      110,      11,      -1;
     -32768,      21504,      14784,    -3080,    -462,      21,     1;
   -2097152,    1409024,     924672,  -211904,  -26488,    1806,    43, -1;
  268435456, -178257920, -119767040, 26199040, 3602368, -204680, -7310, 85, 1;

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. this sequence (q=-2), A158020 (q=-1), A007318 (q=1), A157963 (q=2).
Cf. A135950 (q=2; alternative).
Cf. A022166, A135950.

p[x_, n_, q_]:= q^Binomial[n, 2]*QPochhammer[x, 1/q, n];
Table[CoefficientList[Series[p[x, n, -2], {x,0,n}], x], {n,0,10}]//Flatten (* G. C. Greubel, Nov 29 2021 *)

Sum_{k=0..n} T(n, k) = 0^n.
From G. C. Greubel, Nov 29 2021: (Start)
T(n, k) = [x^k] coefficients of the polynomials defined by q^binomial(n, 2)*QPochhammer(x, 1/q, n), where q = -2.
T(n, k) = [x^k] Product_{j=0..n-1} (q^j - x). (End)

Edited by G. C. Greubel, Nov 29 2021

A157963 Triangle T(n,k), 0<=k<=n, read by rows given by [1,q-1,q^2,q^3-q,q^4,q^5-q^2,q^6,q^7-q^3,q^8,...] DELTA [ -1,0,-q,0,-q^2,0,-q^3,0,-q^4,0,-q^5,0,...] (for q=2) = [1,1,4,6,16,28,64,...] DELTA [ -1,0,-2,0,-4,0,-8,0,-16,0,...] where DELTA is the operator defined in A084938.

Original entry on oeis.org

1, 1, -1, 2, -3, 1, 8, -14, 7, -1, 64, -120, 70, -15, 1, 1024, -1984, 1240, -310, 31, -1, 32768, -64512, 41664, -11160, 1302, -63, 1, 2097152, -4161536, 2731008, -755904, 94488, -5334, 127, -1, 268435456, -534773760, 353730560, -99486720, 12850368

Offset: 0

Philippe Deléham, Mar 10 2009

Row sums equal 0^n.
Row n contains the coefficients of Product_{j=0..n-1} (2^j*x-1), highest coefficient first. - Alois P. Heinz, Mar 26 2012
The elements of the matrix inverse are apparently given by T^(-1)(n,k) = (-1)^k*A022166(n,k). - R. J. Mathar, Mar 26 2013

			Triangle begins :
1;
1,    -1;
2,    -3,  1;
8,   -14,  7,  -1;
64, -120, 70, -15,  1;

Alois P. Heinz, Rows n = 0..44

Cf. A007179, A130595, A157783, A157784, A157785, A157832, A158474.

T:= n-> seq (coeff (mul (2^j*x-1, j=0..n-1), x, n-k), k=0..n):
seq (T(n), n=0..10);  # Alois P. Heinz, Mar 26 2012

row[n_] := CoefficientList[(-1)^n QPochhammer[x, 2, n] + O[x]^(n+1), x] // Reverse; Table[row[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, May 26 2016 *)

T(n,k) = (-1)^n*A135950(n,k). T(n,0) = A006125(n).

T(n,k) = [x^(n-k)] Product_{j=0..n-1} (2^j*x-1). - Alois P. Heinz, Mar 26 2012

A218449 Gaussian binomial coefficient [2*n-1,n] for q=2, n>=0.

Original entry on oeis.org

1, 1, 7, 155, 11811, 3309747, 3548836819, 14877590196755, 246614610741341843, 16256896431763117598611, 4274137206973266943778085267, 4488323837657412597958687922896275, 18839183877670041942218307147122500601235

Offset: 0

Paul D. Hanna, Oct 28 2012

nonn

Compare to: [x^n] Product_{k=0..n-1} 1+2^k*x = 2^(n*(n-1)/2).

			The coefficients in Product_{k=0..n-1} 1/(1 - 2^k*x) begin:
n=0: [(1)];
n=1: [1,(1), 1, 1, 1, 1, 1, 1, 1, 1, ...];
n=2: [1, 3,(7), 15, 31, 63, 127, 255, 511, 1023, ...];
n=3: [1, 7, 35,(155), 651, 2667, 10795, 43435, 174251, ...];
n=4: [1, 15, 155, 1395,(11811), 97155, 788035, 6347715, ...];
n=5: [1, 31, 651, 11811, 200787,(3309747), 53743987, ...];
n=6: [1, 63, 2667, 97155, 3309747, 109221651,(3548836819), ...];
n=7: [1, 127, 10795, 788035, 53743987, 3548836819, 230674393235,(14877590196755), ...]; ...
the coefficients in parenthesis give the initial terms of this sequence;
an adjacent diagonal forms the Gaussian binomial coefficients [2*n,n] for q=2:
[1, 3, 35, 1395, 200787, 109221651, 230674393235, ...] = A006098.

G. C. Greubel, Table of n, a(n) for n = 0..50
Eric Weisstein's World of Mathematics, q-Binomial Coefficient.

Cf. A022166, A006098, A006125.

Table[QBinomial[2n-1, n, 2], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 12 2016 *)

{a(n)=polcoeff(prod(k=0,n-1,1/(1-2^k*x +x*O(x^n))),n)}
for(n=0,20,print1(a(n),", "))

a(n) = [x^n] Product_{k=0..n-1} 1/(1 - 2^k*x).

a(n) ~ c * 2^(n*(n-1)), where c = A065446. - Vaclav Kotesovec, Sep 22 2016

A228465 Recurrence a(n) = a(n-1) + 2^n*a(n-2) with a(0)=0, a(1)=1.

Original entry on oeis.org

0, 1, 1, 9, 25, 313, 1913, 41977, 531705, 22023929, 566489849, 45671496441, 2366013917945, 376506912762617, 39141278944373497, 12376519796349807353, 2577539376694811306745, 1624792742123856760679161, 677311275106408471956040441, 852536648457739021814912002809

Offset: 0

Vaclav Kotesovec, Aug 22 2013

nonn

Generally (if p>0, q>1), recurrence a(n) = b*a(n-1) + (p*q^n+d)*a(n-2), a(n) is asymptotic to c*q^(n^2/4)*(p*q)^(n/2), where c is for fixed parameters b, p, d, q, a(0), a(1) constant, independent on n.

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122.

[n le 2 select (n-1) else Self(n-1)+Self(n-2)*2^(n-1): n in [1..20]]; // Vincenzo Librandi, Aug 23 2013

RecurrenceTable[{a[n]==a[n-1]+2^n*a[n-2],a[0]==0,a[1]==1},a,{n,0,20}]
(* Alternative: *)
a[n_] := Sum[2^(k^2-1) QBinomial[n - k , k - 1, 2], {k, 1, n}];
Table[a[n], {n, 0, 19}] (* After Vladimir Kruchinin. Peter Luschny, Jan 20 2020 *)

def a(n):
    return sum(2^(k^2 - 1)*q_binomial(n-k , k-1, 2) for k in (1..n))
print([a(n) for n in range(20)]) # Peter Luschny, Jan 20 2020

a(n) ~ c * 2^(n^2/4 + n/2), where c = 0.548441579870783378573455400152590154... if n is even and c = 0.800417244834941368929416800341853541... if n is odd.

a(n) = Sum_{k=1..floor(n/2+1/2)} qbinomial(n-k,k-1)*2^(k^2-1), where q-binomial is triangle A022166, that is, with q=2. - Vladimir Kruchinin, Jan 20 2020

A362903 Array read by antidiagonals: T(n,k) is the number of nonisomorphic k-tuples of involutions on a (2n)-set that pairwise commute.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 11, 4, 1, 1, 16, 43, 24, 5, 1, 1, 32, 171, 176, 46, 6, 1, 1, 64, 683, 1376, 611, 80, 7, 1, 1, 128, 2731, 10944, 9281, 1864, 130, 8, 1, 1, 256, 10923, 87424, 146445, 54384, 5161, 200, 9, 1, 1, 512, 43691, 699136, 2334181, 1696352, 285939, 13184, 295, 10, 1

Offset: 0

Andrew Howroyd, May 11 2023

Two involutions x,y commute if x*y = y*x. Isomorphism is up to permutation of the elements of the (2n)-set. T(n,k) also gives the values for a (2n+1)-set.

			Array begins:
======================================================
n/k| 0 1   2     3       4          5            6 ...
---+--------------------------------------------------
0  | 1 1   1     1       1          1            1 ...
1  | 1 2   4     8      16         32           64 ...
2  | 1 3  11    43     171        683         2731 ...
3  | 1 4  24   176    1376      10944        87424 ...
4  | 1 5  46   611    9281     146445      2334181 ...
5  | 1 6  80  1864   54384    1696352     53885632 ...
6  | 1 7 130  5161  285939   17562679   1110290303 ...
7  | 1 8 200 13184 1372224  165343616  20774749952 ...
8  | 1 9 295 31532 6101080 1436647664 358238974304 ...
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)

Columns k=0..3 are A000012, A000027(n-1), A001752, A362904.
Rows n=1..3 are A000079, A007583, A103334(n+1).
Cf. A022166, A362648, A362824, A362826.

\\ B(n, k) is A022166.
B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}
C(k,n) = Vec(1/prod(j=0, min(k-1, logint(n, 2)), (1 - x^(2^j) + O(x*x^n))^B(k,j+1), 1 - x + O(x*x^n)))
M(n,m=n) = Mat(vector(m+1, k, C(k-1, n)~))
{ my(A=M(7)); for(i=1, #A, print(A[i,])) }

G.f. of column k: 1/((1 - x)*Product_{j=0..k-1} (1 - x^(2^j))^A022166(k,j+1)).

A096657 a(n) = (2^n)a(n-1) + (2^(n-1))a(n-2), a(0)=1, a(1)=3.

Original entry on oeis.org

1, 3, 14, 124, 2096, 69056, 4486656, 578711552, 148724449280, 76295068188672, 78202296743231488, 160236429879963287552, 656488575092059763900416, 5378610735570941915498020864, 88128536246001466497105446043648

Offset: 0

Clark Kimberling, Jul 01 2004

nonn

This is the sequence of numerators of self-convergents to the number 1.40861... whose self-continued fraction is (1,2,4,8,16,...)=A000079. See A096658 for denominators and A096654 for definitions.

			a(2)=4*3+2*1=14, a(3)=8*14+4*3=124.

Cf. A000079, A096654, A096658.

a[0] = 1; a[1] = 3; a[n_] := (2^n)*a[n-1] + (2^(n-1))*a[n-2]; Table[ a[n], {n, 0, 14}] (* Robert G. Wilson v, Jul 03 2004 *)
b[n_, k_] := k^2 - k (1 + n) +  n (1 + n)/2;
a[n_] := Sum[2^b[n, k] QBinomial[n - k + 1, k, 2], {k, 0, n + 1}] ;
Table[a[n], {n, 0, 14}] (* After Vladimir Kruchinin, Peter Luschny, Jan 19 2020 *)

a(n) is asymptotic to c*2^(n(n+1)/2) where c = 2.1726687508496636560169136... - Benoit Cloitre, Jul 02 2004
c = 1 + Sum_{k>=1} (Product_{j=1..k} 1/(2^(j-1)*(2^j-1))) = 2.172668750849663656016913609859312820656436935109608860295... . - Vaclav Kotesovec, Nov 27 2015
a(n) = Sum_{k=0..n+1} q-binomial(n-k+1,k)*2^(binomial(n-k+1,2)+binomial(k,2)), where q-binomial is triangle A022166, that is, with q=2. - Vladimir Kruchinin, Jan 19 2020

More terms from Benoit Cloitre, Jul 02 2004

A288853 Triangle read by rows: T(n,k) is the number of surjective linear mappings from an n-dimensional vector space over F_2 onto a k-dimensional vector space, n>=0, 0<=k<=n.

Original entry on oeis.org

1, 1, 1, 1, 3, 6, 1, 7, 42, 168, 1, 15, 210, 2520, 20160, 1, 31, 930, 26040, 624960, 9999360, 1, 63, 3906, 234360, 13124160, 629959680, 20158709760, 1, 127, 16002, 1984248, 238109760, 26668293120, 2560156139520, 163849992929280, 1, 255, 64770, 16322040, 4047865920, 971487820800, 217613271859200, 41781748196966400, 5348063769211699200

Offset: 0

Geoffrey Critzer, Jun 18 2017

The (q = 2) analog of A008279.
A022166(m,k)*T(n,k) is the number of m X n matrices over F_2 that have rank k.
a(n) is the number of n X n matrices over F_2 in Green's R class containing A where rank(A) = k. - Geoffrey Critzer, Oct 05 2022

			  1;
  1,  1;
  1,  3,   6;
  1,  7,  42,   168;
  1, 15, 210,  2520,  20160;
  1, 31, 930, 26040, 624960, 9999360;
  ...

Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
Jeremy L. Martin, Lecture Notes on Algebraic Combinatorics, 2010-2023, Example 2.3.6.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
Wikipedia, Green's relations.

Columns k=0-10 give: A000012, A000225, 6*A006095, 168*A006096, 20160*A006097, 9999360*A006110, 20158709760*A022189, 163849992929280*A022190, 5348063769211699200*A022191, 699612310033197642547200*A022192, 366440137299948128422802227200*A022193.
Main diagonal gives A002884.
Cf. A022166.

Table[Table[Product[q^n - q^i, {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0,8}] // Grid

T(n,k) = Product_{j=0..k-1} (2^n - 2^j).
T(n,k) = A002884(k)*A022166(n,k).
Let g_m(x) = Sum_{n>=0} (2^m*x)^n/A005329(n) and e(x) = Sum_{n>=0} x^n/A005329(n).  Then Sum_{k>=0} T(n,k)*x^k/A005329(k) = g_n(x)/e(x). - Geoffrey Critzer, Jun 01 2024

A305737 Number of subsets S of vectors in GF(2)^n such that span(S) = GF(2)^n.

Original entry on oeis.org

1, 2, 8, 184, 62464, 4293001088, 18446743803209556992, 340282366920938461120638132973980614656, 115792089237316195423570985008687907766497981100801256254562260326801824546816

Offset: 0

Geoffrey Critzer, Jun 22 2018

nonn

Asymptotic to A001146(n) = 2^(2^n).

R. P. Stanley, Enumerative Combinatorics Vol 1, Cambridge, 1997, page 127.

Andrew Howroyd, Table of n, a(n) for n = 0..10
Tilman Piesk, relationship to Boolean functions (Wikiversity)

Cf. A001146, A022166, A158474, A051179.

Table[Sum[QBinomial[n, k, q] (-1)^(n - k) q^Binomial[n - k, 2] (2^(q^k) - 1) /. q -> 2, {k, 0, n}], {n, 0, 8}]

\\ here U(n,k) is A022166(n,k).
U(n,k)={polcoeff(x^k/prod(j=0, k, 1-2^j*x+x*O(x^n)), n)}
a(n)={sum(k=0, n, U(n,k)*(-1)^(n-k)*2^binomial(n-k,2)*(2^(2^k)-1))} \\ Andrew Howroyd, Mar 01 2020

a(n) = Sum_{k=0..n} A022166(n,k)*(-1)^(n-k)*2^binomial(n-k,2)*(2^(2^k)-1).
Sum_{k=0..n} a(k)* A022166(n,k) = 2^(2^n) - 1. - Geoffrey Critzer, Apr 25 2024
a(n) = Sum_{k=0..n} A158474(n,k) * A051179(n-k). - Tilman Piesk, Mar 12 2025

a(8) corrected by Andrew Howroyd, Mar 01 2020

A342186 Triangle read by rows, matrix inverse of A139382.

Original entry on oeis.org

1, -1, 1, 3, -4, 1, -21, 31, -11, 1, 315, -486, 196, -26, 1, -9765, 15381, -6562, 1002, -57, 1, 615195, -978768, 428787, -69688, 4593, -120, 1, -78129765, 124918731, -55434717, 9279163, -652999, 19833, -247, 1

Offset: 1

John Keith, Mar 04 2021

This triangle appears to be the q-analog of A008275 (Stirling numbers of the first kind) for q=2. However, A333142 has a similar definition.
Row sums of unsigned triangle are A006125 with offset 1.
|T(n,k)| is the number of descent free digraphs on [n] containing exactly k source nodes.  A descent in a digraph is a pair of vertices s->t such that s>t.  A descent free digraph is necessarily acyclic.  A source in an acyclic digraph is a node with indegree 0. - Geoffrey Critzer, Mar 05 2025

			The triangle begins:
           1;
          -1,         1;
           3,        -4,         1;
         -21,        31,       -11,       1;
         315,      -486,       196,     -26,       1;
       -9765,     15381,     -6562,    1002,     -57,     1;
      615195,   -978768,    428787,  -69688,    4593,  -120,    1;
   -78129765, 124918731, -55434717, 9279163, -652999, 19833, -247, 1;
  ...

John Keith, Rows n = 1..20 of triangle, flattened
Kassie Archer, Ira M. Gessel, Christina Graves, and Xuming Liang, Counting acyclic and strong digraphs by descents, arXiv:1909.01550 [math.CO], 20 Mar 2020.

Cf. A008275, A139382, A333142, A333143, A006125 (row sums).

Columns of unsigned triangle: A005329, A203011, A000295, A203242.

A342186 := proc(n, k) if n = 1 and k = 1 then 1 elif k > n or k < 1 then 0 else
A342186(n-1, k-1) - (2^(n-1) - 1) * A342186(n-1, k) fi end:
for n from 1 to 8 do seq(A342186(n, k), k = 1..n) od; # Peter Luschny, Jun 28 2022

T[1, 1] := 1; T[n_, k_] := T[n, k] = If[k > n || k < 1, 0, T[n - 1, k - 1] - (2^(n - 1) - 1)*T[n - 1, k]]; Table[T[n, k], {n, 1, 8}, {k, 1, n}] (* after G. C. Greubel's program for A139382 *)

mat(nn) = my(m = matrix(nn, nn)); for (n=1, nn, for(k=1, nn, m[n,k] = if (n==1, if (k==1, 1, 0), if (k==1, 1, (2^k-1)*m[n-1, k] + m[n-1, k-1])););); m; \\ A139382
tabl(nn) = 1/mat(nn); \\ Michel Marcus, Mar 18 2021

T(n,k) = T(n-1,k-1) - (2^(n-1)-1) * T(n-1,k), n, k >= 1, T(1, 1) = 1, T(n, 0) = 0.
For unsigned triangle, T(n, 1) = A005329(n-1); T(n, 2) = A203011(n-1); T(n, n-1) = A000295(n+1); T(n, n-2) = A203242(n-1).
T(n,k) = Sum_{j=k..n} (-1)^(n-j)*2^binomial(n-j,2)*qBinomial(n,j,2)*binomial(j,k), where qBinomial(n,k,2) is A022166(n,k). - Fabian Pereyra, Feb 08 2024

A347485 Irregular triangle read by rows: T(n, k) is the q-multinomial coefficient defined by the k-th partition of n in Abramowitz-Stegun order, evaluated at q = 2.

Original entry on oeis.org

1, 1, 3, 1, 7, 21, 1, 15, 35, 105, 315, 1, 31, 155, 465, 1085, 3255, 9765, 1, 63, 651, 1395, 1953, 9765, 22785, 29295, 68355, 205065, 615195, 1, 127, 2667, 11811, 8001, 82677, 177165, 413385, 248031, 1240155, 2893695, 3720465, 8681085, 26043255, 78129765

Offset: 1

Álvar Ibeas, Sep 03 2021

Abuse of notation: we write T(n, L) for T(n, k), where L is the k-th partition of n in A-St order.

For any permutation (e_1,...,e_r) of the parts of L, T(n, L) is the number of chains of subspaces 0 < V_1 < ··· < V_r = (F_2)^n with dimension increments (e_1,...,e_r).

			The number of subspace chains 0 < V_1 < V_2 < (F_2)^3 is 21 = T(3, (1, 1, 1)). There are 7 = A022166(3, 1) choices for a one-dimensional subspace V_1 and, for each of them, 3 = A022166(2, 1) extensions to a two-dimensional subspace V_2.
Triangle begins:
  k:  1  2   3   4    5    6    7
      ---------------------------
n=1:  1
n=2:  1  3
n=3:  1  7  21
n=4:  1 15  35 105  315
n=5:  1 31 155 465 1085 3255 9765

R. P. Stanley, Enumerative Combinatorics (vol. 1), Cambridge University Press (1997), Section 1.3.

Álvar Ibeas, First 20 rows, flattened

Cf. A036038 (q = 1), A022166, A005329 (last entry in each row).

T(n, (n)) = 1. T(n, L) = A022166(n, e) * T(n - e, L \ {e}), if L is a partition of n and e < n is a part of L.

cp's OEIS Frontend

A157785 Triangle of coefficients of the polynomials defined by q^binomial(n, 2)*QPochhammer(x, 1/q, n), where q = -2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A157963 Triangle T(n,k), 0<=k<=n, read by rows given by [1,q-1,q^2,q^3-q,q^4,q^5-q^2,q^6,q^7-q^3,q^8,...] DELTA [ -1,0,-q,0,-q^2,0,-q^3,0,-q^4,0,-q^5,0,...] (for q=2) = [1,1,4,6,16,28,64,...] DELTA [ -1,0,-2,0,-4,0,-8,0,-16,0,...] where DELTA is the operator defined in A084938.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A218449 Gaussian binomial coefficient [2*n-1,n] for q=2, n>=0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A228465 Recurrence a(n) = a(n-1) + 2^n*a(n-2) with a(0)=0, a(1)=1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A362903 Array read by antidiagonals: T(n,k) is the number of nonisomorphic k-tuples of involutions on a (2n)-set that pairwise commute.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A096657 a(n) = (2^n)*a(n-1) + (2^(n-1))*a(n-2), a(0)=1, a(1)=3.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions

A288853 Triangle read by rows: T(n,k) is the number of surjective linear mappings from an n-dimensional vector space over F_2 onto a k-dimensional vector space, n>=0, 0<=k<=n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

A096657 a(n) = (2^n)a(n-1) + (2^(n-1))a(n-2), a(0)=1, a(1)=3.