OFFSET
0,2
FORMULA
a(n) = N(5; n, -1) with polynomials N(5; n, x) defined in A062986.
a(n) = Sum(((-1)^(n-j))*2^(4*j+1)*A002294(j), j=1..n)+(-1)^n, with A002294(j) = A062993(j+3, 3) = binomial(5*j, j)/(4*j+1).
From Vaclav Kotesovec, Sep 04 2026: (Start)
Recurrence: n*(2*n - 1)*(4*n - 1)*(4*n + 1)*a(n) = (6218*n^4 - 12484*n^3 + 8752*n^2 - 2501*n + 240)*a(n-1) + 10*(5*n - 4)*(5*n - 3)*(5*n - 2)*(5*n - 1)*a(n-2).
a(n) ~ 5^(5*n + 11/2) / (3141 * sqrt(Pi) * n^(3/2) * 2^(4*n + 5/2)). (End)
MATHEMATICA
Table[(-1)^n + Sum[(-1)^(n-j) * 2^(4*j+1) * Binomial[5*j, j] / (4*j+1), {j, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 04 2026 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wolfdieter Lang, Jul 12 2001
STATUS
approved