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A259763 Number of symmetric n X n (0,1)-matrices with pairwise distinct rows and columns. 14
1, 2, 6, 44, 716, 24416, 1680224, 229468288, 61820527104, 32848197477760, 34502874046006912, 71850629135663531776, 297429744309497638961920, 2452504520881914016303901696, 40340635076928240671195746599936, 1324981038432182976845483456362661888, 86953044949519288083916385603832568137728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..80

MathOverflow, Counting matrices of special types, 2015.

FORMULA

a(n) = Sum_{k=0..n} stirling1(n,k) * 2^(k*(k+1)/2).

MATHEMATICA

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

PROG

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

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

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

Sequence in context: A058925 A266855 A171690 * A219337 A259482 A255015

Adjacent sequences:  A259760 A259761 A259762 * A259764 A259765 A259766

KEYWORD

nonn

AUTHOR

Max Alekseyev, Jul 04 2015

EXTENSIONS

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

STATUS

approved

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Last modified January 19 20:33 EST 2019. Contains 319310 sequences. (Running on oeis4.)