OFFSET
0,2
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..139 (terms 0..70 from Alois P. Heinz)
FORMULA
a(n) = A255982(2n,n).
a(n) ~ c * d^n * n!^2 / n^(5/2), where d = A256254 = 98.8248737517356857317..., c = 2^(3/8) * (-LambertW(-2*exp(-2)))^(1/8) / (8 * Pi^(3/2) * sqrt(1 + LambertW(-2*exp(-2)))) = 0.033762267258894908009578351704834892... . - Vaclav Kotesovec, May 31 2015, updated Sep 27 2023
EXAMPLE
a(1) = 2 : [||-], [-||].
MAPLE
b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
end:
A:= proc(n, k) option remember; `if`(n=0, 1,
-add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
end:
T:= proc(n, k) option remember;
add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
end:
a:= n-> T(2*n, n):
seq(a(n), n=0..15);
MATHEMATICA
b[n_, k_, t_] := b[n, k, t] = If[t == 0, 1, If[t == 1, A[n - 1, k], Sum[A[j, k]*b[n - j - 1, k, t - 1], {j, 0, n - 2}]]]; A[n_, k_] := A[n, k] = If[n == 0, 1, -Sum[Binomial[k, j]*(-1)^j*b[n + 1, k, 2^j], {j, 1, k}]]; T[n_, k_] := T[n, k] = Sum[A[n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}]; a[n_] := T[2*n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Dec 18 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 29 2015
STATUS
approved