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A361626
Expansion of e.g.f. exp( x/(1-x)^3 ) / (1-x)^2.
2
1, 3, 17, 139, 1437, 17711, 252133, 4059567, 72779129, 1435276027, 30836352441, 716101686323, 17858449006357, 475653606922599, 13467411746316557, 403708230041927191, 12767545998797849073, 424670548932688771187, 14814998283177691422049
OFFSET
0,2
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(n+2*k+1,n-k)/k! = Sum_{k=0..n} (n+2*k+1)!/(3*k+1)! * binomial(n,k).
a(n) ~ 3^(5/8) * exp(-1/27 - 3^(3/4)*n^(1/4)/72 + sqrt(3*n)/6 + 4*3^(-3/4)*n^(3/4) - n) * n^(n + 3/8) / 6 * (1 + 63037 * 3^(1/4)/(69120 * n^(1/4))). - Vaclav Kotesovec, Mar 29 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^3)/(1-x)^2))
(PARI) a(n)=n! * sum(k=0, n, binomial(n+2*k+1, n-k)/k!) \\ Winston de Greef, Mar 18 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2023
STATUS
approved