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A196958 E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Sum_{k=0..n} (-1)^(n-k) * C(n,k) * (1 + x/A(x)^k)^k. 1
1, 1, -3, 22, -227, 2571, -19157, -550675, 47287609, -2474401796, 113036728791, -4672627704315, 162246902824213, -2986895872839215, -218043087879704765, 36487218926663045686, -3474880515053581779215, 262843589524537015935667, -15730145172651453469201745, 541394288749029235105442821 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

E.g.f. satisfies: A(x) = Sum_{n>=0} A(x)^(-n^2) * exp(1/A(x)^n - 1)*x^n/n!.

EXAMPLE

E.g.f.: A(x) = 1 + x - 3*x^2/2! + 22*x^3/3! - 227*x^4/4! + 2571*x^5/5! +...

where:

A(x) = 1 + 1/A(x)*exp(1/A(x) - 1)*x + 1/A(x)^4*exp(1/A(x)^2 - 1)*x^2/2! + 1/A(x)^9*exp(1/A(x)^3 - 1)*x^3/3! + 1/A(x)^16*exp(1/A(x)^4 - 1)*x^4/4! +...

Also, e.g.f. A = A(x) satisfies:

A(x) = 1 - (1 - (1+x/A)) + 1/2!*(1 - 2*(1+x/A) + (1+x/A^2)^2) -

1/3!*(1 - 3*(1+x/A) + 3*(1+x/A^2)^2 - (1+x/A^3)^3) +

1/4!*(1 - 4*(1+x/A) + 6*(1+x/A^2)^2 - 4*(1+x/A^3)^3 + (1+x/A^4)^4) -

1/5!*(1 - 5*(1+x/A) + 10*(1+x/A^2)^2 - 10*(1+x/A^3)^3 + 5*(1+x/A^4)^4 - (1+x/A^5)^5) +-...

PROG

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, exp(A^(-m)-1)*A^(-m^2)*X^m/m!)); n!*polcoeff(A, n)}

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

CROSSREFS

Cf. A195947, A196959.

Sequence in context: A173142 A073530 A120667 * A274246 A161567 A213109

Adjacent sequences:  A196955 A196956 A196957 * A196959 A196960 A196961

KEYWORD

sign

AUTHOR

Paul D. Hanna, Oct 08 2011

STATUS

approved

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)