A108367 L(n,-n), where L is defined as in A108299.

1, -2, 5, -29, 265, -3191, 47321, -832040, 16908641, -389806471, 10049731549, -286482047279, 8946795882025, -303762892305614, 11140078609864049, -438857301101610929, 18482410314337295233, -828657053219851847135, 39406519321199703822581, -1981132660316876165976260

Offset

0,2

Comments

A108366(n) = L(n,n).

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Morgan-Voyce polynomials

Formula

a(n) = (-1)^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} (-1)^k*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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, 2*k)*(n+2)^k); \\ Jinyuan Wang, Feb 25 2020

Crossrefs

Cf. A000312, A085478, A108299, A108366.

Sequence in context: A007014 A265147 A098682 * A191621 A103592 A209428

Adjacent sequences: A108364 A108365 A108366 * A108368 A108369 A108370

Keyword

sign

Author

Reinhard Zumkeller, Jun 01 2005

Extensions

More terms from Jinyuan Wang, Feb 25 2020

Status

approved