A301770 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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