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A143921 E.g.f. A(x) satisfies: A(x) = exp(x + x*Integral A(x) dx). 1
1, 1, 3, 10, 49, 281, 1975, 15933, 147457, 1528282, 17603351, 222691261, 3072168481, 45882929925, 737717712439, 12703639993306, 233281370579713, 4550465650811445, 93966210612477271, 2047838398486924977 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit n->infinity (a(n)/n!)^(1/n) = 1.1453530527... - Vaclav Kotesovec, Feb 24 2014

Compare to: G(x) = exp(Integral G(x) dx) when G(x) = 1/(1-x).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

FORMULA

E.g.f. A(x) satisfies: log(A(x)) = x*A'(x)/A(x) - x^2*A(x).

EXAMPLE

E.g.f. A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 49*x^4/4! + 281*x^5/5! +...

log(A(x)) = x + x^2 + x^3/2! + 3*x^4/3! + 10*x^5/4! + 49*x^6/5! +...

A'(x)/A(x) = 1 + 2*x + 3*x^2/2! + 12*x^3/3! + 50*x^4/4! + 294*x^5/5! +...

PROG

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

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Sequence in context: A220362 A005921 A193281 * A082426 A054381 A102088

Adjacent sequences:  A143918 A143919 A143920 * A143922 A143923 A143924

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 06 2008

STATUS

approved

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Last modified December 6 06:58 EST 2016. Contains 278775 sequences.