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A354286
Expansion of e.g.f. 1/(1 - x)^(2/(1 + 2 * log(1-x))).
3
1, 2, 14, 144, 1936, 32000, 625952, 14117152, 360175584, 10246079616, 321313928448, 11006050602624, 408662128569984, 16344011453662464, 700254206319007488, 31990601456727585792, 1551985176120589820928, 79669906174753878177792
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A088500(k) * binomial(n-1,k-1) * a(n-k).
a(n) = Sum_{k=0..n} 2^k * A000262(k) * |Stirling1(n,k)|.
a(n) ~ n^(n - 1/4) / (2^(3/4) * (exp(1/2) - 1)^(n + 1/4) * exp(3/4 - 1/(4*(exp(1/2) - 1)) - sqrt(2*n/(exp(1/2) - 1)) + n/2)). - Vaclav Kotesovec, May 23 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^(2/(1+2*log(1-x)))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 2^k*k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 23 2022
STATUS
approved