A129440 -id:A129440 - cp's OEIS frontend

A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.

2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Number of nonisomorphic complete binary trees with leaves colored using two colors. - Brendan McKay, Feb 01 2001

With a(0) = 2, a(n+1) is the number of possible distinct sums between any number of elements in {1,...,a(n)}. - Derek Orr, Dec 13 2014

			Example for depth 2 (the nonisomorphic possibilities are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
         o
        / \
       /   \
      o     o
     / \   / \
    /   \ /   \
    A   B B   B

W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 0..12
G. L. Honaker, Jr., 41041 (another Prime Pages' Curiosity)
J. C. Kieffer, Hierarchical Type Classes and Their Entropy Functions, in 2011 First International Conference on Data Compression, Communications and Processing, pp. 246-254; Digital Object Identifier: 10.1109/CCP.2011.36.
J. V. Post, Math Pages [wayback copy]
J.S. Seneschal, Iteration of Complete Graphs
Stephan Wagner, Enumeration of highly balanced trees

Cf. A000217, A006893.
Cf. A117872 (parity), A275342 (2-adic valuation).
Cf. A129440.
Cf. A013589 (start=4), A050542 (start=5), A050548 (start=7), A050536 (start=8), A050909 (start=9).
Cf.  A108225, A145272.

a007501 n = a007501_list !! n
a007501_list = iterate a000217 2  -- Reinhard Zumkeller, Aug 15 2013

f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]

PARI
```
a(n)=if(n<1,2,a(n-1)*(1+a(n-1))/2)
```

a(n) = A006893(n+1) + 1.
a(n+1) = A000217(a(n)). - Reinhard Zumkeller, Aug 15 2013
a(n) ~ 2 * c^(2^n), where c = 1.34576817070125852633753712522207761954658547520962441996... . - Vaclav Kotesovec, Dec 17 2014
a(n) = A145272(n) + a(n-1). - J.S. Seneschal, Jul 17 2025

A251702 a(1)=5, a(n) = a(n-1)(a(n-1)-1)(a(n-1)-2)/6.

Original entry on oeis.org

5, 10, 120, 280840, 3691654113991480, 8385167839605753859676710992399730619003333960

Offset: 1

Frank M Jackson, Dec 07 2014

nonn

In general, sequence a(n) = binomial(a(n-1),k) is asymptotic to (k!)^(1/(k-1)) * c^(k^n), where the constant c is dependent on k and a(1). For big a(1), c asymptotically approaches (a(1)/(k!)^(1/(k-1)))^(1/k). - Vaclav Kotesovec, Dec 09 2014

			a(2) = a(1)*(a(1)-1)*(a(1)-2)/6 = 5*4*3/6 = 10.

Vaclav Kotesovec, Table of n, a(n) for n = 1..8

Cf. A086714, A251792, A129440, A086714.

RecurrenceTable[{a[1] == 5, a[n] == a[n - 1](a[n - 1] - 1)(a[n - 1] - 2)/6}, a[n], {n, 10}]

Limit_{n->oo} a(n)^(1/3^n) = 1.1546796279605837888382808629570944052320556413... (see A251792).
a(n) ~ sqrt(6) * A251792^(3^n). - Vaclav Kotesovec, Dec 09 2014
a(n) = binomial(a(n-1),3) for n >= 1. - Shel Kaphan, Feb 06 2023

cp's OEIS Frontend

A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.

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A251702 a(1)=5, a(n) = a(n-1)(a(n-1)-1)(a(n-1)-2)/6.

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cp's OEIS Frontend

A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

A251702 a(1)=5, a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)-2)/6.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A251702 a(1)=5, a(n) = a(n-1)(a(n-1)-1)(a(n-1)-2)/6.