OFFSET
1,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Graph Path
Eric Weisstein's World of Mathematics, Path Complement Graph
FORMULA
a(n) = (1/2)*Sum_{k=2..n} Sum_{i=1..k} Sum_{j=0..k-i} (-1)^(k-i)*i!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j). - Andrew Howroyd, Apr 21 2018
a(n) ~ n! / (2*exp(1)). - Vaclav Kotesovec, Apr 22 2018
MATHEMATICA
Array[(1/2) Sum[Sum[Sum[(-1)^(k - i) i!*2^j*Binomial[# + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {j, 0, k - i}], {i, k}], {k, 2, #}] &, 23] (* Michael De Vlieger, Apr 21 2018 *)
Table[Sum[(-1)^(k - i) i! 2^j Binomial[n + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {k, 2, n}, {i, k}, {j, 0, k - i}]/2, {n, 20}] (* Eric W. Weisstein, Apr 23 2018 *)
PROG
(PARI) a(n)={sum(k=2, n, sum(i=1, k, sum(j=0, min(i, k-i), (-1)^(k-i)*i!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j))))/2} \\ Andrew Howroyd, Apr 21 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 12 2018
EXTENSIONS
Terms a(15) and beyond from Andrew Howroyd, Apr 21 2018
STATUS
approved