OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = exp( -2/5 * LambertW(-5*x/2 * exp(5*x/2)) ).
E.g.f.: A(x) = ( -LambertW(-5*x/2 * exp(5*x/2)) / (5*x/2 * exp(5*x/2)) )^(2/5).
E.g.f.: A(x) = ( Sum_{k>=0} (k+1)^(k-1) * (5*x/2 * exp(5*x/2))^k / k! )^(2/5).
a(n) = Sum_{k=0..n} (5*k/2)^(n-k) * (5*k/2+1)^(k-1) * binomial(n,k).
a(n) ~ sqrt(1 + LambertW(exp(-1))) * 5^(n-1) * n^(n-1) / (exp(n - 2/5) * 2^(n-1) * LambertW(exp(-1))^n). - Vaclav Kotesovec, May 06 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2/5*lambertw(-5/2*x*exp(5*x/2)))))
(PARI) a(n) = sum(k=0, n, (5*k/2)^(n-k)*(5*k/2+1)^(k-1)*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 25 2024
STATUS
approved