A129824 -id:A129824 - cp's OEIS frontend

A217716 Duplicate of A129824.

2, 4, 12, 64, 700, 17424, 1053696, 160579584, 62856336636, 63812936890000, 168895157342195152, 1169048914836855865344, 21209591746609937928524800, 1010490883477487017627972550656, 126641164340871500483202065902080000

Offset: 0

Jon Perry, Mar 21 2013

dead

Number of words less than or equal to the concatenation of the n-th row of Pascal's Triangle.
a(n) = 2 * A055612(n). - Reinhard Zumkeller, Jan 31 2015
Same as A129824. - Georg Fischer, Oct 14 2018

			Row 2 is 1 2 1 and we have 000, 001, 010, 011, 020, 021, 100, 101, 110, 111, 120 and 121 so a(2)=12.

Reinhard Zumkeller, Table of n, a(n) for n = 0..69

Table[Product[Binomial[n, k] + 1, {k, 0, n}], {n, 0, 15}] (* T. D. Noe, Mar 21 2013 *)

a(n) = Product_{k=0..n} (binomial(n,k) + 1).

A055612 a(n) = Product_{m=1..n} (binomial(n,m)+1).

Original entry on oeis.org

1, 2, 6, 32, 350, 8712, 526848, 80289792, 31428168318, 31906468445000, 84447578671097576, 584524457418427932672, 10604795873304968964262400, 505245441738743508813986275328, 63320582170435750241601032951040000, 20908669294849228879861552351685432573952

Offset: 0

N. J. A. Sloane, Jun 03 2000

nonn

V. K. Kharchenko, Fixed rings and noncommutative invariant theory, pp. 359-398 of M. Hazewinkel, ed., Handbook of Algebra, Vol. 2, Elsevier, 2000.

Reinhard Zumkeller, Table of n, a(n) for n = 0..69

Cf. A007318, A217716, A293954, A293955.

a055612 = product . map (+ 1) . tail . a007318_row
-- Reinhard Zumkeller, Jan 31 2015

Array[Product[1 + Binomial[#, m], {m, #}] &, 16, 0] (* Michael De Vlieger, Oct 30 2017 *)

a(n) = prod(m=1, n, 1+binomial(n, m)); \\ Michel Marcus, Oct 30 2017

a(n) = A129824(n) / 2. - Reinhard Zumkeller, Jan 31 2015

cp's OEIS Frontend

A217716 Duplicate of A129824.

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A055612 a(n) = Product_{m=1..n} (binomial(n,m)+1).

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