OFFSET
0,4
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..250
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
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 2*x)) / (1 - 2*x). - Ilya Gutkovskiy, Jan 30 2022
MAPLE
bintr:= proc(p) local b;
b:=proc(n) option remember; add (p(k)*binomial(n, k), k=0..n) end
end:
b:= (bintr@@2)(a):
a:= n-> `if`(n<2, 1, b(n-2)):
seq (a(n), n=0..30); # Alois P. Heinz, Oct 18 2012
MATHEMATICA
bintr[p_] := Module[{b}, b[n_] := b[n] = Sum [p[k]*Binomial[n, k], {k, 0, n}]; b]; b = a // bintr // bintr; a[n_] := If[n<2, 1, b[n-2]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 27 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,nice,eigen
AUTHOR
STATUS
approved