OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = A341279(2n,n).
a(n) ~ c * d^n / sqrt(n), where d = 3.03044218957412050685579849718626198523346... and c = 0.2319377657497495246637662111041144... - Vaclav Kotesovec, Feb 20 2021
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
[1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, g(n+1),
(q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30); # Alois P. Heinz, Feb 07 2021
MATHEMATICA
Table[SeriesCoefficient[(-1 + 1/QPochhammer[-x, x])^n, {x, 0, 2 n}], {n, 0, 30}]
A[n_, k_] := A[n, k] = If[n == 0, 1, -k Sum[A[n - j, k] Sum[Mod[d, 2] d, {d, Divisors[j]}], {j, 1, n}]/n]; T[n_, k_] := Sum[(-1)^i Binomial[k, i] A[n, k - i], {i, 0, k}]; Table[T[2 n, n], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2021
STATUS
approved