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A229188 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (A(x) - x^k). 1
1, 1, 1, 3, 7, 21, 60, 181, 557, 1741, 5531, 17778, 57741, 189191, 624634, 2076037, 6940372, 23322865, 78739090, 266933783, 908335157, 3101467309, 10622722567, 36486959455, 125652837052, 433761554314, 1500704852813, 5202773031536, 18072036054031, 62886222829136, 219194323393547 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 3.66153677891582..., c = 0.464274715544... . - Vaclav Kotesovec, Oct 29 2014

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 21*x^5 + 60*x^6 + 181*x^7 +...

where the g.f. A = A(x) satisfies:

A(x) = 1 + x*(A-x) + x^2*(A-x)*(A-x^2) + x^3*(A-x)*(A-x^2)*(A-x^3) + x^4*(A-x)*(A-x^2)*(A-x^3)*(A-x^4) + x^5*(A-x)*(A-x^2)*(A-x^3)*(A-x^4)*(A-x^5) +...

PROG

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

for(n=0, 40, print1(a(n), ", "))

CROSSREFS

Sequence in context: A096240 A182887 A035080 * A091486 A056779 A183113

Adjacent sequences:  A229185 A229186 A229187 * A229189 A229190 A229191

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 15 2013

STATUS

approved

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Last modified March 28 15:03 EDT 2020. Contains 333089 sequences. (Running on oeis4.)