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