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A362314
a(n) = n! * Sum_{k=0..floor(n/4)} (n/4)^k /(k! * (n-4*k)!).
5
1, 1, 1, 1, 25, 151, 541, 1471, 84001, 925345, 5682601, 25177681, 2245355641, 35901100951, 312222474565, 1917363070351, 232479594721921, 4873115730725761, 54830346428307601, 430468886732009185, 65997947903313461401, 1711564302775814535511
OFFSET
0,5
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^4/4).
E.g.f.: exp( ( -LambertW(-x^4) )^(1/4) ) / (1 + LambertW(-x^4)).
From Vaclav Kotesovec, Apr 18 2023: (Start)
a(n) ~ c * n^n / exp(3*n/4), where
c = cosh(1) + cos(1) if mod(n,4)=0,
c = sinh(1) + sin(1) if mod(n,4)=1,
c = cosh(1) - cos(1) if mod(n,4)=2,
c = sinh(1) - sin(1) if mod(n,4)=3. (End)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^4))^(1/4))/(1+lambertw(-x^4))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved