A381506 Expansion of e.g.f. exp(3*x/4) / (1-4*x)^(1/16).

1, 1, 2, 12, 138, 2202, 44172, 1064664, 29947644, 962720316, 34812065304, 1398413067984, 61779789904248, 2976866834860728, 155364530441352912, 8730749828092965408, 525584335643810008848, 33743905825099188235536, 2301524700814009677800736

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} (-4)^k * (3/4)^(n-k) * binomial(-1/16,k)/(n-k)!.

a(n) = (4*n-3)*a(n-1) - 3*(n-1)*a(n-2) for n > 1.

a(n) ~ sqrt(Pi) * n^(n - 7/16) * 2^(2*n + 1/2) / (Gamma(1/16) * exp(n - 3/16)). - Vaclav Kotesovec, Apr 23 2025

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*x/4)/(1-4*x)^(1/16)))

Crossrefs

Cf. A002801, A381505.

Sequence in context: A117513 A343439 A297078 * A185522 A119819 A330655

Adjacent sequences: A381503 A381504 A381505 * A381507 A381508 A381509

Keyword

nonn

Author

Seiichi Manyama, Apr 23 2025

Status

approved