OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100
FORMULA
a(n) = f(n) + SUM{((n-i)^(n-i-2))*C((n-1), i)*a(i):i=1, 2, ..(n-1)}, where f(n)=number of forests on labeled vertex set [n], A001858.
Exponential convolution of A000272 and A001858: a(n) = Sum_{k=1..n} binomial(n, k)*k^(k-2)*A001858(n-k). E.g.f.: B(x)*exp(B(x)), where B(x) is e.g.f. for A000272. - Vladeta Jovovic, May 24 2005
a(n) = Sum_{m=1..n} A105599(n,m)*m. - Geoffrey Critzer, Nov 04 2012
EXAMPLE
a(5) = 291 + (16*4*1)+(3*6*3)+(1*4*12)+(1*1*68) = 525.
MAPLE
B:= n-> exp(add(k^(k-2) *x^k/k!, k = 1..n )): b:= n-> coeff(series(B(n), x, n+1), x, n)*n!: a:= n-> add(binomial(n, k) *k^(k-2) *b(n-k), k=1..n): seq(a(n), n=1..25); # Alois P. Heinz, Sep 10 2008
MATHEMATICA
nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Drop[Range[0, nn]!CoefficientList[Series[D[Exp[y(t-t^2/2)], y]/.y->1, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Nov 04 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph G. Moser (jmoser(AT)wcupa.edu), Jan 26 2005
EXTENSIONS
More terms from Alois P. Heinz, Sep 10 2008
STATUS
approved