OFFSET
2,1
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107.
G.f.: A(x) = B(x)^2*(2-B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic, Oct 19 2001
MAPLE
b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-1)^2*(2-B(n-1))/(1-B(n-1))^3, x=0, n+1), x, n): seq(a(n), n=2..25); # Alois P. Heinz, Aug 21 2008
MATHEMATICA
b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[b[n+1 - j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := Coefficient[Series[B[n-1]^2*((2 - B[n-1])/ (1 - B[n-1])^3), {x, 0, n+1}], x, n]; Table[a[n], {n, 2, 25}] (* Jean-François Alcover, Dec 20 2012, translated from Alois P. Heinz's Maple program *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms, new description and formula from Christian G. Bower, Nov 15 1999
STATUS
approved