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A184360 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} (n+1)!^2*(x/2)^n. 3
1, 2, 5, 34, 442, 8638, 229467, 7862664, 336468450, 17579403622, 1101881183359, 81669937516066, 7070184169543820, 707266516140720872, 80989516005804384644, 10528134125581145088720, 1542184766049169920609018 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

G.f. satisfies: A(x) = G(x/A(x)) where A(x*G(x)) = G(x) = Sum_{n>=0} (n+1)!^2*(x/2)^n.

G.f. satisfies: [x^n] A(x)^(n+1)/(n+1) = (n+1)!^2/2^n = A184358(n).

EXAMPLE

G.f.: A(x) = 1 + 2*x + 5*x^2 + 34*x^3 + 442*x^4 + 8638*x^5 +...

A(x)^(1/2) = 1 + x + 2*x^2 + 15*x^3 + 204*x^4 + 4085*x^5 + 110128*x^6 +...+ A184361(n)*x^n +...

The g.f. of A184358 is G(x) = A(x*G(x)):

G(x) = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 + 396900*x^6 +...+ (n+1)!^2*x^n/2^n +...

PROG

(PARI) {a(n)=polcoeff(x/serreverse(x*sum(m=0, n+1, (m+1)!^2*(x/2)^m)+x^2*O(x^n)), n)}

CROSSREFS

Cf. A184361, A184358, A182958.

Sequence in context: A356772 A307143 A052695 * A283111 A206830 A277436

Adjacent sequences: A184357 A184358 A184359 * A184361 A184362 A184363

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 16 2011

STATUS

approved

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Last modified January 30 14:06 EST 2023. Contains 359945 sequences. (Running on oeis4.)