OFFSET
5,1
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.
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
Vincenzo Librandi, Table of n, a(n) for n = 5..200
FORMULA
G.f.: A(x) = B(x)^5*(125-204*B(x)+118*B(x)^2-24*B(x)^3)/(1-B(x))^7, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.
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-4)^5* (125-204*B(n-4) +118*B(n-4)^2 -24*B(n-4)^3)/ (1-B(n-4))^7, x=0, n+1), x, n): seq(a(n), n=5..23); # 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_] := SeriesCoefficient[B[n-4]^5*(125 - 204*B[n-4] + 118*B[n-4]^2 - 24*B[n-4]^3)/(1 - B[n-4])^7, {x, 0, n}]; Table[a[n], {n, 5, 23}] (* Jean-François Alcover, Mar 20 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Oct 19 2001
STATUS
approved