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A155804 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n-1)/2). 5
1, 1, 1, 4, 19, 161, 1606, 21022, 323485, 5874913, 122077756, 2871573596, 75437801539, 2193468714373, 70020045331510, 2437979768144026, 92073099488632441, 3753886179551636513, 164556499026975482008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..18.

FORMULA

E.g.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:

B(x) = Sum_{n>=0} x^n/n! * B(x)^(n*(n+1)/2) and is the e.g.f. of A155805.

EXAMPLE

E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! +...

where e.g.f. A(x) satisfies:

A(x) = 1 + x + x^2/2!*A(x) + x^3/3!*A(x)^3 + x^4/4!*A(x)^6 + x^5/5!*A(x)^10 +...

Let B(x) = A(x*B(x)) be the e.g.f. of A155805 then:

B(x) = 1 + x*B(x) + x^2/2!*B(x)^3 + x^3/3!*B(x)^6 + x^4/4!*B(x)^10 +...

B(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! + 47392*x^6/6! +...

PROG

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

CROSSREFS

Cf. A155805, A155806, A155807, A107590, A219358.

Sequence in context: A225904 A203010 A249785 * A292167 A126147 A007411

Adjacent sequences:  A155801 A155802 A155803 * A155805 A155806 A155807

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 27 2009

STATUS

approved

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Last modified January 17 12:18 EST 2020. Contains 330958 sequences. (Running on oeis4.)