OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
Eric Weisstein's World of Mathematics, Graph Path
FORMULA
a(n) = Sum_{k=2..2*n} n!^2/((n-ceiling(k/2))!*(n-floor(k/2))!). - Andrew Howroyd, Jun 10 2017
a(n) = n!^2 * Sum_{k=0..n-1} (1 + k)/(k!^2). - Andrew Howroyd, Feb 24 2023
MATHEMATICA
Table[Sum[(n!)^2/((n - Ceiling[k/2])! (n - Floor[k/2])!), {k, 2, 2 n}], {n, 20}] (* Eric W. Weisstein, Jun 13 2017 *)
Table[n!^2 (BesselI[0, 2] + BesselI[1, 2] - HypergeometricPFQRegularized[{1}, {1 + n, 1 + n}, 1]) - n HypergeometricPFQ[{1}, {n, 1 + n}, 1], {n, 20}] // FunctionExpand (* Eric W. Weisstein, Jun 13 2017 *)
PROG
(PARI) a(n) = sum(k=2, 2*n, n!^2/((n-(k+1)\2)!*(n-k\2)!)); \\ Andrew Howroyd, Jun 10 2017
(PARI) a(n) = n!^2*sum(k=0, n-1, (1 + k)/(k!)^2) \\ Andrew Howroyd, Feb 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 04 2017
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Jun 10 2017
STATUS
approved