A159311 G.f. A(x) satisfies: Sum_{n>=0} n!*x^n/A(x)^n = 1/(1-x).

1, 1, 2, 6, 26, 150, 1066, 8862, 83506, 874302, 10035538, 125082870, 1680770250, 24211249062, 372151797498, 6080329604238, 105238649649762, 1923853815102030, 37047429233963170, 749689860387252966

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..446

Formula

G.f. satisfies: A(x) = exp( Sum_{n>=1} [(n-1)*a(n) + 1]*x^n/n ).

G.f. satisfies: x*A'(x) = A(x)*(1/(1-x) - A(x))/(1 - A(x)).

G.f.: A(x) = x/Series_Reversion(G(x)) so that G(x/A(x)) = x where G(x) = g.f. of A003319 (indecomposable permutations).

a(n) ~ n*n!/exp(1) * (1 - 2/n - 3/n^2 - 49/(3*n^3) - 379/(3*n^4) - 18509/(15*n^5)). - Vaclav Kotesovec, Aug 01 2015

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 150*x^5 + 1066*x^6 +...
log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 79*x^4/4 + 601*x^5/5 + 5331*x^6/2 +...
where coefficients of log(A(x)) is given by (n-1)*a(n) + 1:
3 = 1*2 + 1, 13 = 2*6 + 1, 79 = 3*26 + 1, 601 = 4*15 + 1, 5331 = 5*1066 + 1.
Let G(x) = g.f. of A003319, then G(x/A(x)) = x where:
G(x) = x + x^2 + 3*x^3 + 13*x^4 + 71*x^5 + 461*x^6 + 3447*x^7 +...
and G(x) = 1 - 1/(1 + x + 2!*x^2 + 3!*x^3 + 4!*x^4 +...).

Prog

(PARI) {a(n)=local(G003319=1-1/sum(k=0, n+1, k!*x^k+x^2*O(x^n))); polcoeff(x/serreverse(G003319), n)}

Crossrefs

Cf. A003319, A159312.

Sequence in context: A247224 A052859 A103937 * A000629 A185994 A032187

Adjacent sequences: A159308 A159309 A159310 * A159312 A159313 A159314

Keyword

nonn

Author

Paul D. Hanna, Apr 16 2009

Status

approved