A288703 Number of (undirected) paths in the n-barbell graph.

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

Andrew Howroyd, Table of n, a(n) for n = 1..50

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

Adjacent sequences: A288700 A288701 A288702 * A288704 A288705 A288706

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