OFFSET
4,1
REFERENCES
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
Colin Barker, Table of n, a(n) for n = 4..1000
J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).
FORMULA
a(n) = n(n-1)*S2(n-2, 2) where S2(n, k) denotes the Stirling numbers of 2nd kind. - Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 19 2001
a(n) = n*(n-1)*(2^(n-3) - 1) = 2*A000217(n-1)*A000225(n-3). - Robert G. Wilson v, Jul 01 2007, corrected by Ilya Gutkovskiy, Sep 17 2016
a(n) = Sum_{k=1..n-3} binomial(n,2)*binomial(n-2,k). The sum gives the number of Prüfer sequences with exactly 2 distinct digits. - Geoffrey Critzer, Sep 17 2016
E.g.f.: (x*(exp(x)-1))^2/2. - Geoffrey Critzer, Sep 17 2016
O.g.f.: 2*x^4*(6 - 24*x + 33*x^2 - 18*x^3 + 4*x^4)/((1 - x)^3*(1 - 2*x)^3). - Ilya Gutkovskiy, Sep 17 2016
a(n) = (2^n-8)*(n-1)*n/8. - Colin Barker, Sep 18 2016
MATHEMATICA
f[n_] := n (n - 1)*StirlingS2[n - 2, 2]; Table[ f@n, {n, 4, 29}] (* Robert G. Wilson v, Jul 01 2007 *)
PROG
(PARI) Vec(2*x^4*(6-24*x+33*x^2-18*x^3+4*x^4)/((1-x)^3*(1-2*x)^3) + O(x^40)) \\ Colin Barker, Sep 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jul 01 2007
STATUS
approved