A179325 G.f.: A(x) = x*exp( Sum_{n>=1} A(A(x)^n)/n ).

1, 1, 3, 12, 59, 331, 2062, 13945, 100981, 775099, 6260336, 52914052, 466062718, 4263629043, 40404127710, 395772643255, 4000017157615, 41650278419675, 446222379390064, 4913287373304033, 55545290608129184, 644152152145611596

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

Euler transform equals A192637.

G.f. A(x) satisfies: Series_Reversion(A(x)) = x*Product_{n>=1} (1 - x^n)^a(n), where A(x) = Sum_{n>=1} a(n)*x^n.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 59*x^5 + 331*x^6 + 2062*x^7 +...
Log(A(x)/x) = A(A(x)) + A(A(x)^2)/2 + A(A(x)^3)/3 + A(A(x)^4)/4 +...
Log(A(x)/x) = x + 5*x^2/2 + 28*x^3/3 + 181*x^4/4 + 1271*x^5/5 + 9596*x^6/6 + 76665*x^7/7 + 642941*x^8/8 +...+ A179326(n)*x^n/n +...
The g.f. also satisfies:
x = A( x*(1-x)*(1-x^2)*(1-x^3)^3*(1-x^4)^12*(1-x^5)^59*(1-x^6)^331*... ).

Prog

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

Crossrefs

Cf. A179326, A192637.

Sequence in context: A058861 A105668 A192768 * A064856 A080337 A196710

Adjacent sequences: A179322 A179323 A179324 * A179326 A179327 A179328

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2010

Status

approved