A194004 E.g.f.: A(x) = -log(3-exp(x)-exp(x^2)).

0, 1, 4, 12, 86, 590, 6032, 66948, 913754, 13855542, 239928992, 4579666916, 96564964322, 2216227508118, 55168605200984, 1478010072581076, 42439794637684826, 1299629513716412246, 42289878531064635632, 1456983891928235324292, 52986585444052122288146

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n!*sum(k=1..n, (k-1)!*sum(j=0..k, sum(m=floor((k-j)/2)..(n-j)/2, (stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!))))).

a(n) ~ (n-1)!/r^n, where r = 0.522452131474223... is the root of the equation exp(r)+exp(r^2) = 3. - Vaclav Kotesovec, Jun 27 2013

Mathematica

CoefficientList[Series[-Log[3-E^x-E^(x^2)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Prog

(Maxima)
a(n):=n!*sum((k-1)!*sum(sum((stirling2(n-2*m, j)*stirling2(m, k-j))/((n-2*m)!*(m!)), m, floor((k-j)/2), (n-j)/2), j, 0, k), k, 1, n);

Crossrefs

Sequence in context: A226960 A081214 A331087 * A064280 A203379 A209031

Adjacent sequences: A194001 A194002 A194003 * A194005 A194006 A194007

Keyword

nonn

Author

Vladimir Kruchinin, Aug 10 2011

Status

approved