A259763 Number of symmetric n X n (0,1)-matrices with pairwise distinct rows and columns.

1, 2, 6, 44, 716, 24416, 1680224, 229468288, 61820527104, 32848197477760, 34502874046006912, 71850629135663531776, 297429744309497638961920, 2452504520881914016303901696, 40340635076928240671195746599936, 1324981038432182976845483456362661888, 86953044949519288083916385603832568137728

Offset: 0

Author

Max Alekseyev, Jul 04 2015

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..80
• MathOverflow, Counting matrices of special types, 2015.

Crossrefs

Cf. A088310, A006024

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

Programs

Magma

[(&+[StirlingFirst(n,k)*2^Binomial(k+1,2): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Nov 04 2018

Mathematica

Table[Sum[StirlingS1[n,k]*2^Binomial[k+1,2], {k,0,n}], {n,0,20}] (* G. C. Greubel, Nov 04 2018*)

PARI

A259763(n) = sum(k=1,n, stirling(n,k,1) * 2^(k*(k+1)/2) );

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * 2^(k*(k+1)/2).

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 12 2015