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A353548 Expansion of e.g.f. -log(1-4*x) * exp(x)/4. 4
0, 1, 6, 47, 540, 8429, 166210, 3952955, 109981816, 3502905369, 125648153278, 5011458069639, 219987094389524, 10538817637744005, 547118005892177018, 30595552548140425747, 1833501625083035349488, 117219490267316310468913 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n-1} 4^(n-1-k) / ((n-k) * k!).
a(0) = 0, a(1) = 1, a(n) = (4 * n - 3) * a(n-1) - 4 * (n-1) * a(n-2) + 1.
a(n) ~ (n-1)! * exp(1/4) * 4^(n-1). - Vaclav Kotesovec, Jun 08 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-4*x)*exp(x)/4)))
(PARI) a(n) = n!*sum(k=0, n-1, 4^(n-1-k)/((n-k)*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(4*i-3)*v[i]-4*(i-1)*v[i-1]+1); v;
CROSSREFS
Cf. A346396.
Essentially partial sums of A056545.
Sequence in context: A307567 A368270 A332238 * A192887 A321190 A320403
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 27 2022
STATUS
approved

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Last modified May 24 14:39 EDT 2024. Contains 372778 sequences. (Running on oeis4.)