OFFSET
0,5
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1900
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
FORMULA
Shifts left when weigh-transform applied twice.
a(n) ~ c * d^n / n^(3/2), where d = 3.382016466020272807429818743..., c = 0.161800727760188847021075748... . - Vaclav Kotesovec, Jul 26 2014
MAPLE
g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*g(n-i*j, i-1), j=0..n/i)))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(g(i, i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<1, 0, b(n-1, n-1)):
seq(a(n), n=0..40); # Alois P. Heinz, May 19 2013
MATHEMATICA
g[n_, i_] := g[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := If[n<1, 0, b[n-1, n-1]]; Table[a[n] // FullSimplify, {n, 0, 40}] (* Jean-François Alcover, Feb 11 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,nice,eigen
AUTHOR
EXTENSIONS
Additional comments from Christian G. Bower
STATUS
approved