A369723 Expansion of e.g.f. exp( 2 * (1-sqrt(1-4*x)) ).

1, 4, 24, 208, 2464, 37824, 720256, 16450816, 439245312, 13440572416, 464007387136, 17847329869824, 757011972726784, 35108108023349248, 1767517592731090944, 96007679735852498944, 5596725706163142393856, 348533116657888468402176

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Cf. A001517, A101682, A243953, A369722, A369724.

Cf. A000108.

Sequence in context: A010039 A245407 A162314 * A323869 A112141 A077555

Adjacent sequences: A369720 A369721 A369722 * A369724 A369725 A369726

Keyword

nonn

Author

Seiichi Manyama, Jan 30 2024

Status

approved