OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
Recurrence: see Maple program.
a(n) ~ c*r^n/sqrt(Pi*n), where r = 3.408698199842151... is the root of the equation 4 - 32*r - 8*r^2 + 5*r^3 = 0 and c = 0.479880052557486135... is the root of the equation 1 + 384*c^2 - 2368*c^4 + 2960*c^6 = 0. - Vaclav Kotesovec, Nov 27 2013
EXAMPLE
a(1) = 1: [2].
a(2) = 4: [2,2], [1,2,1], [2,1,1], [1,1,2].
a(3) = 5: [2,2,2], [1,3,1,1], [1,1,3,1], [3,1,1,1], [1,1,1,3].
a(4) = 21: [2,2,2,2], [1,1,4,1,1], [4,1,1,1,1], [1,4,1,1,1], [1,1,1,4,1], [1,1,1,1,4], [1,2,1,1,1,2], [2,1,1,1,1,2], [2,1,2,1,1,1], [1,2,2,1,1,1],[1,2,1,2,1,1], [2,1,1,2,1,1], [1,2,1,1,2,1], [2,1,1,1,2,1],[1,1,2,1,2,1], [1,1,2,2,1,1], [2,2,1,1,1,1], [1,1,1,2,2,1], [1,1,2,1,1,2], [1,1,1,2,1,2], [1,1,1,1,2,2].
MAPLE
a:= proc(n) option remember;
`if`(n<5, [1, 1, 4, 5, 21][n+1],
((n-1)*(14911*n^4 -102036*n^3 +249203*n^2
-252880*n +87794) *a(n-1)
+(27528*n^5 -239548*n^4 +803564*n^3 -1283816*n^2
+963472*n -266160) *a(n-2)
-2*(2*n-5)*(10323*n^4 -62876*n^3 +136848*n^2
-125584*n +40329) *a(n-3)
+2*(2*n-7)*(n-2)*(1147*n^3 -4055*n^2 +4742*n
-1762) *a(n-4)) / (5*(n-1)*n*
(1147*n^3 -7496*n^2 +16293*n -11706)))
end:
seq(a(n), n=0..35);
MATHEMATICA
b[n_, s_] := b[n, s] = If[n == 0, 1, If[n<s, 0, Expand[Sum[b[n-j, s]*x, {j, s, n}]]]]; T[n_, k_] := If[k == 0, If[n == 0, 1, 0], Sum[Function[{p}, Sum[ Coefficient[p, x, i]*Binomial[i+k, k], {i, 0, Exponent[p, x]}]][b[n-j*k, j+1]], {j, 1, n/k}]]; a[n_] := T[2n, n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 09 2015, after A238342 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 27 2013
STATUS
approved