OFFSET
0,4
COMMENTS
A108367(n) = L(n,-n).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..386
Eric Weisstein's World of Mathematics, Morgan-Voyce polynomials
FORMULA
a(n) = Product_{k=1..n} (n - 2*cos((2*k-1)*Pi/(2*n+1))) with Pi = 3.14...
a(n) = Sum_{k=0..n} binomial(n+k,2*k)*(n-2)^k = b(n,n-2), where b(n,x) are the Morgan-Voyce polynomials of A085478. - Peter Bala, May 01 2012
a(n) ~ n^n * (1 - 2/n + 5/(2*n^2) - 31/(6*n^3) + 209/(24*n^4) - 173/(10*n^5) + ...). - Vaclav Kotesovec, Jan 06 2021
MATHEMATICA
Join[{1, 0, 1}, Table[Sum[Binomial[n + k, 2*k] * (n-2)^k, {k, 0, n}], {n, 3, 20}]] (* Vaclav Kotesovec, Jan 06 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+k, 2*k)*(n-2)^k); \\ Jinyuan Wang, Feb 25 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 01 2005
EXTENSIONS
More terms from Jinyuan Wang, Feb 25 2020
STATUS
approved