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A288703
Number of (undirected) paths in the n-barbell graph.
1
1, 6, 37, 316, 4545, 108226, 3843541, 187799592, 12013365601, 973014552190, 97300597043301, 11773360632193876, 1695363763070006497, 286516473369031084986, 56157228737911538160085, 12635376465294288199302976, 3234656375101858631647453761, 934815692404177059563237280502
OFFSET
1,2
COMMENTS
Should be straightforward to give a formula in terms of path counts on complete graph K_n.
Sequence extended to n=1 using formula. - Andrew Howroyd, Jun 19 2017
LINKS
Eric Weisstein's World of Mathematics, Barbell Graph
Eric Weisstein's World of Mathematics, Graph Path
FORMULA
a(n) = A000522(n-1)^2 + A000522(n) - n - 1. - Andrew Howroyd, Jun 19 2017
MATHEMATICA
Table[E (E Gamma[n, 1]^2 + Gamma[n + 1, 1]) - n - 1, {n, 20}]
PROG
(PARI)
b(n)=sum(i=0, n, n!/i!);
a(n)=b(n-1)^2 + b(n) - n - 1; \\ Andrew Howroyd, Jun 19 2017
CROSSREFS
Cf. A000522.
Sequence in context: A218298 A179515 A330495 * A337552 A036358 A340029
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 13 2017
EXTENSIONS
a(1)-a(2) and a(10)-a(18) from Andrew Howroyd, Jun 19 2017
STATUS
approved