The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A368597 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A368597

Number of n-element sets of singletons or pairs of distinct elements of {1..n} with union {1..n}, or loop-graphs covering n vertices with n edges.
(history; published version)

#15 by Michael De Vlieger at Sat Feb 24 11:03:20 EST 2024

STATUS

proposed

approved

#14 by Gus Wiseman at Sat Feb 24 10:00:33 EST 2024

STATUS

editing

proposed

#13 by Gus Wiseman at Sat Feb 24 06:42:35 EST 2024

CROSSREFS

The connected case is A368951.

Cf. A000272, A000666, A057500, A066383, A333331, A367869, A368596, A368600, A368928, A368951, A369199.

STATUS

approved

editing

#12 by OEIS Server at Sat Jan 06 12:06:51 EST 2024

LINKS

Andrew Howroyd, <a href="/A368597/b368597_1.txt">Table of n, a(n) for n = 0..200</a>

#11 by Michael De Vlieger at Sat Jan 06 12:06:51 EST 2024

STATUS

proposed

approved

Discussion

Sat Jan 06

12:06

OEIS Server: Installed first b-file as b368597.txt.

#10 by Andrew Howroyd at Sat Jan 06 11:29:46 EST 2024

STATUS

editing

proposed

#9 by Andrew Howroyd at Sat Jan 06 11:27:58 EST 2024

DATA

1, 1, 3, 17, 150, 1803, 27364, 501015, 10736010, 263461265, 7283725704, 223967628066, 7581128184175, 280103206674480, 11216492736563655, 483875783716549277, 22371631078155742764, 1103548801569848115255, 57849356643299101021960, 3211439288584038922502820

LINKS

MathWorld, Andrew Howroyd, <a href="https://mathworld.wolfram.comA368597/GraphLoopb368597_1.htmltxt">Graph LoopTable of n, a(n) for n = 0..200</a>.

Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphLoop.html">Graph Loop</a>.

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(binomial(k+1,2), n). - Andrew Howroyd, Jan 06 2024

PROG

(PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n, k) * binomial(binomial(k+1, 2), n)) \\ Andrew Howroyd, Jan 06 2024

EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Jan 06 2024

STATUS

approved

editing

#8 by Michael De Vlieger at Sat Jan 06 09:18:43 EST 2024

STATUS

reviewed

approved

#7 by Joerg Arndt at Sat Jan 06 08:43:22 EST 2024

STATUS

proposed

reviewed

#6 by Gus Wiseman at Sat Jan 06 08:32:34 EST 2024

STATUS

editing

proposed