A053294 a(0)=1, a(m+1) = Sum_{k=0..m}[a(k)^2 * a(m-k)^2].

1, 1, 2, 9, 170, 57978, 6722955416, 90396259057770600841, 16342967303279146791599896178138243550346

Offset

0,3

Comments

a(9) = 5.341...*10^80 is too large to include in the data section. - Amiram Eldar, Oct 02 2021

Links

Michael De Vlieger, Table of n, a(n) for n = 0..12

Jean-Marc Luck, Revisiting log-periodic oscillations, arXiv:2403.00432 [cond-mat.stat-mech], 2024. See p. 7.

Example

a(4)= a(0)^2*a(3)^2 + a(1)^2*a(2)^2 + a(2)^2*a(1)^2 + a(3)^2*a(0)^2 = 1^2*9^2 + 1^2*2^2 + 2^2*1^2 + 9^2*1^2 = 170.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[a[k]^2*a[n - 1 - k]^2, {k, 0, n - 1}]; Array[a, 9, 0] (* Amiram Eldar, Oct 02 2021 *)

Crossrefs

Sequence in context: A038843 A367526 A237201 * A199695 A349691 A078524

Adjacent sequences: A053291 A053292 A053293 * A053295 A053296 A053297

Keyword

nonn

Author

Leroy Quet, Mar 04 2000

Status

approved