A379688 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 2*x*exp(x)) ).

1, 2, 20, 366, 9992, 365130, 16769292, 929022206, 60323670416, 4494465562770, 378025706776340, 35434198578761862, 3663111561838580568, 414057463231218044186, 50805545997014472821276, 6725525908390393438264590, 955435863749903677193184032, 144987884255349864723586105122

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..326

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 2^(n-k) * (n-k)^k * (2*n-k)!/(k! * (n-k)!).

E.g.f. A(x) satisfies A(x) = 1/( 1 - 2*x*A(x)*exp(x*A(x)) ).

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380095.

a(n) ~ (s-1)^(n + 1/2) * s^(n+1) * n^(n-1) / (sqrt(4*s - 2 - s^2) * exp(n) * (2-s)^n), where s = 1.840999254165862013788496667520425971530532392938... is the root of the equation 2*s*(2-s) * exp((2-s)/(s-1)) = (s-1)^2. - Vaclav Kotesovec, Feb 04 2026

Prog

(PARI) a(n) = sum(k=0, n, 2^(n-k)*(n-k)^k*(2*n-k)!/(k!*(n-k)!))/(n+1);

Crossrefs

Cf. A213644, A380097.

Cf. A379659, A379687.

Cf. A380095.

Sequence in context: A382505 A267827 A084948 * A187661 A263207 A376391

Adjacent sequences: A379685 A379686 A379687 * A379689 A379690 A379691

Keyword

nonn

Author

Seiichi Manyama, Dec 29 2024

Status

approved