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A365782 Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(1/4). 1
1, 1, 7, 79, 1273, 26761, 694207, 21426679, 766897873, 31228168561, 1425551226007, 72103869999679, 4002503339419273, 241916116809963961, 15814645240322565007, 1111830805751346135079, 83649120614618202845473, 6705916845517938558372961 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (4*j+1)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (2 - 3/2 * k/n) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = a(n-1) - 3*Sum_{k=1..n-1} (-2)^k * binomial(n-1,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 4*j+1)*stirling(n, k, 2));
CROSSREFS
Sequence in context: A186377 A112700 A365039 * A362773 A235370 A098105
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 16 2023
STATUS
approved

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Last modified May 27 08:37 EDT 2024. Contains 372850 sequences. (Running on oeis4.)