A381504 Expansion of e.g.f. exp(-x/4) / (1-4*x)^(1/16).

1, 0, 1, 8, 99, 1616, 32815, 797256, 22552873, 728069984, 26413495281, 1063820511080, 47098650935611, 2273501091042288, 118834339196361919, 6686552010270859496, 402975635704196998545, 25897425517232941658816, 1767875520978811381774753, 127753191169784612437640904

Offset

0,4

Links

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

Formula

a(n) = (-1)^n * n! * Sum_{k=0..n} (1/4)^(n-2*k) * binomial(-1/16,k)/(n-k)!.

a(n) = (n-1) * (4*a(n-1) + a(n-2)) for n > 1.

a(n) ~ sqrt(Pi) * 2^(2*n + 1/2) * n^(n - 7/16) / (Gamma(1/16) * exp(n + 1/16)). - Vaclav Kotesovec, Apr 23 2025

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x/4)/(1-4*x)^(1/16)))

Crossrefs

Cf. A000166, A383313, A381484.

Sequence in context: A388135 A341965 A230343 * A376101 A293145 A305919

Adjacent sequences: A381501 A381502 A381503 * A381505 A381506 A381507

Keyword

nonn

Author

Seiichi Manyama, Apr 23 2025

Status

approved