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A268171 E.g.f. A(x) satisfies: A(x) = exp(1+x - exp(x)) * exp( Integral C(x) dx )  such that C(x) = exp( Integral A(x) dx ), where the constant of integration is zero. 1
1, 1, 1, 2, 9, 46, 245, 1474, 10315, 82174, 726591, 7038632, 74216949, 847103658, 10407684559, 136932309578, 1920656913247, 28609816527534, 451057722743007, 7503877147726572, 131368238149821145, 2414204385183262842, 46469039032487849079, 934915621488296098358, 19624030747998750863203 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Compare to: F(x) = exp( Integral G(x) dx ) such that G(x) = exp(1-exp(x)) * exp( Integral F(x) dx ) holds when F(x) = exp(x).

LINKS

Table of n, a(n) for n=0..24.

FORMULA

Logarithmic derivative of A268170.

EXAMPLE

E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 9*x^4/4! + 46*x^5/5! + 245*x^6/6! + 1474*x^7/7! + 10315*x^8/8! + 82174*x^9/9! + 726591*x^10/10! + 7038632*x^11/11! + 74216949*x^12/12! +...

where

C(x) = 1 + x + 2*x^2/2! + 5*x^3/3! + 16*x^4/4! + 65*x^5/5! + 326*x^6/6! + 1947*x^7/7! + 13410*x^8/8! + 104181*x^9/9! + 900214*x^10/10! + 8566655*x^11/11! +...+ A268170(n)*x^n/n! +...

and A(x) and C(x) satisfy:

(1) A(x) = C'(x)/C(x),

(2) C(x) = A'(x)/A(x) + exp(x) - 1,

(3) log(C(x)) = Integral A(x) dx,

(4) log(A(x)) = Integral C(x) dx + 1+x - exp(x).

PROG

(PARI) {a(n) = my(A=1+x, C=1+x); for(i=0, n,  A = exp(1+x - exp(x +x*O(x^n))) * exp( intformal( C + x*O(x^n) ) ); C = exp( intformal( A ) );  ); n!*polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Sequence in context: A074607 A251178 A162725 * A168431 A036726 A219197

Adjacent sequences:  A268168 A268169 A268170 * A268172 A268173 A268174

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 29 2016

STATUS

approved

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Last modified July 30 16:50 EDT 2021. Contains 346359 sequences. (Running on oeis4.)