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A365777 Expansion of e.g.f. (exp(2*x) / (2 - exp(2*x)))^(3/4). 2
1, 3, 15, 117, 1257, 17163, 284055, 5522877, 123344817, 3111071283, 87454712895, 2710961144037, 91862770847577, 3378032307195003, 133970268354806535, 5699864583381903597, 258956671286986317537, 12512342291081486212323, 640686944845321006836975 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-2)^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-2)^k * (1/2 * k/n - 2) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 3*a(n-1) + 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+3)*stirling(n, k, 2));
CROSSREFS
Cf. A365794.
Sequence in context: A245043 A225109 A080290 * A369722 A259843 A136654
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 16 2023
STATUS
approved

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Last modified February 23 13:42 EST 2024. Contains 370283 sequences. (Running on oeis4.)