A301770 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x^2*A(x)^2/(1 - x*A(x) - 2*x^2*A(x)^2/(1 - x*A(x) - 3*x^2*A(x)^2/(1 - ...)))), a continued fraction.

1, 1, 3, 11, 47, 217, 1061, 5399, 28337, 152381, 835823, 4660779, 26357111, 150872165, 872878665, 5098306063, 30034591105, 178326873753, 1066472979083, 6421120346267, 38907397325295, 237182461204097, 1454326514077709, 8968048205494983, 55608797571427793, 346716786105033077

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = [x^n] (Sum_{k>=0} A000085(k)*x^k)^(n+1)/(n + 1).

Example

G.f. A(x) = 1 + x + 3*x^2 + 11*x^3 + 47*x^4 + 217*x^5 + 1061*x^6 + 5399*x^7 + 28337*x^8 + ...

Mathematica

Table[SeriesCoefficient[(1 + Sum[(I/Sqrt[2])^k * HermiteH[k, -I/Sqrt[2]] * x^k, {k, 1, n}])^(n+1)/(n+1), {x, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Nov 05 2021 *)

Crossrefs

Cf. A000085, A224922, A301409.

Sequence in context: A151161 A227846 A124890 * A308227 A247313 A262607

Adjacent sequences: A301767 A301768 A301769 * A301771 A301772 A301773

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 26 2018

Status

approved