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A194937 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^n/sf(n) where A(x) = Sum_{n>=0} a(n)*x^n/sf(n), and sf(n) = Product_{k=0..n} k! is the superfactorial of n (A000178). 0
1, 1, 3, 31, 1393, 330361, 488337121, 5197945772881, 452395544496860161, 360573039112103480718721, 2914843277842193790386417088001, 262261378512171017948642290003977004801, 285983731923953608933716749772942709840131379201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..12.

FORMULA

G.f.: A(x) = (1/x)*Series_Reversion(x/F(x)) where F(x) = Sum_{n>=0} x^n/sf(n) and sf(n) = Product_{k=0..n} k!.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2/(1!*2!) + 31*x^3/(1!*2!*3!) + 1393*x^4/(1!*2!*3!*4!) + 330361*x^5/(1!*2!*3!*4!*5!) + 488337121*x^6/(1!*2!*3!*4!*5!*6!) +...

where

A(x) = 1 + x*A(x) + x^2*A(x)^2/(1!*2!) + x^3*A(x)^3/(1!*2!*3!) + x^4*A(x)^4/(1!*2!*3!*4!) +...

PROG

(PARI) {a(n)=local(F=sum(m=0, n, x^m/prod(k=0, m, k!)+x*O(x^n))); prod(k=0, n, k!)*polcoeff(1/x*serreverse(x/F), n)}

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^m/prod(k=0, m, k!))); prod(k=0, n, k!)*polcoeff(A, n)}

CROSSREFS

Cf. A000178.

Sequence in context: A319253 A328811 A136584 * A141153 A144906 A081789

Adjacent sequences: A194934 A194935 A194936 * A194938 A194939 A194940

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 05 2011

STATUS

approved

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Last modified January 29 15:06 EST 2023. Contains 359923 sequences. (Running on oeis4.)