A181088 a(n) = A181089(2*n+1,n)/(n+2).

1, -4, -40, 672, 8064, -253440, -3294720, 153753600, 2091048960, -130025226240, -1820353167360, 141707492720640, 2024392753152000, -189483161695027200, -2747505844577894400, 300609462994993152000, 4408938790593232896000

Offset

0,2

Comments

What are the constraints on left-right symmetric triangles t(n,m) such that t(2*n,n)/(n+1) are integers?

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

a(n) = (A060821(2*n+1, n) + A060821(2*n+1, n+1))/(n+2). - G. C. Greubel, Apr 04 2021

Mathematica

(* First program *)
p[x_, n_] = HermiteH[n, x] + ExpandAll[x^n*HermiteH[n, 1/x]];
b:= Table[CoefficientList[p[x, n], x], {n, 0, 50}];
Table[b[[2*n+2, n+1]]/(n+2), {n, 0, 20}]
(* Second program *)
A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*2^k*n!/(k!*(Floor[(n - k)/2]!)), 0];
a[n_]:= (A060821[2*n+1, n] + A060821[2*n+1, n+1])/(n+2);
Table[a[n], {n, 0, 25}] (* G. C. Greubel, Apr 04 2021 *)

Prog

(Sage)
def A060821(n, k): return (-1)^((n-k)//2)*2^k*factorial(n)/(factorial(k)*factorial( (n-k)//2)) if (n-k)%2==0 else 0
def a(n): return (A060821(2*n+1, n) + A060821(2*n+1, n+1))/(n+2)
[a(n) for n in (0..25)] # G. C. Greubel, Apr 04 2021

Crossrefs

Cf. A060821, A177042, A177043, A181089.

Sequence in context: A343446 A205671 A234294 * A005431 A153849 A372232

Adjacent sequences: A181085 A181086 A181087 * A181089 A181090 A181091

Keyword

sign

Author

Roger L. Bagula, Oct 02 2010

Status

approved