A129440 a(0)=0, a(1)=1, a(2)=5 and for n>2: a(n) = a(n-1)*(a(n-1) + 1)*(2*a(n-1) + 1)/6.

0, 1, 5, 55, 56980, 61667666167030, 78172010815921069181209893626754427513955

Offset: 0

Author

Reinhard Zumkeller, Apr 15 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..8

Crossrefs

Cf. A000330, A007501, A251702.

Programs

Magma

[0,1] cat [n le 1 select 5 else Self(n-1)*(Self(n-1)+1)*(2*Self(n-1)+1)/6: n in [1..8]]; // G. C. Greubel, Feb 06 2024

Mathematica

Flatten[{0, 1, RecurrenceTable[{a[2] == 5, a[n] == a[n-1]*(a[n-1] + 1)*(2*a[n-1] + 1)/6}, a[n], {n, 8}]}] (* Vaclav Kotesovec, Dec 17 2014 *)
Join[{0,1},NestList[(#(#+1)(2#+1))/6&,5,5]] (* Harvey P. Dale, Sep 13 2022 *)

SageMath

def a(n): # a = A129440
    if n<3: return (0,1,5)[n]
    else: return a(n-1)*(a(n-1)+1)*(2*a(n-1)+1)/6
[a(n) for n in range(9)] # G. C. Greubel, Feb 06 2024

Formula

a(n) = A000330(if n<=2 then n else a(n)).

a(n) ~ sqrt(3) * c^(3^n), where c = 1.13701835838072682283814038264701129587627956851233106833915157... . - Vaclav Kotesovec, Dec 17 2014