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A369723
Expansion of e.g.f. exp( 2 * (1-sqrt(1-4*x)) ).
2
1, 4, 24, 208, 2464, 37824, 720256, 16450816, 439245312, 13440572416, 464007387136, 17847329869824, 757011972726784, 35108108023349248, 1767517592731090944, 96007679735852498944, 5596725706163142393856, 348533116657888468402176
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = Sum_{k=0..n-1} 4^(n-k) * (n-1+k)! / (k! * (n-1-k)!).
a(n) = 2*(2*n-3)*a(n-1) + 16*a(n-2).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*(1-sqrt(1-4*x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 30 2024
STATUS
approved