
COMMENTS

If the terms in each row of a Pascal's triangle (see the tabular presentation of A007318) 1, 11, 121, 1331, 14641, 15101051, 1615201561, 172135352171 are concatenated (if necessary) and considered as palindromes, represented in different bases, then A051920(n) for n>=0 could be considered as the smallest base radix for which those palindromes are composed of single digits/letters. Those palindromes will look like: 1, 11, 121, 1331, 14641, 15AA51, 16FKF61, 17LZZL71, ... . Conversion of such palindromes from their above mentioned bases to decimal yields this sequence of the consecutive ascending powers. Such powers are enumerations of the rows in a Pascal's triangle, counting from 0, namely: 1, 3, 16, 125, 4096, 248832, 113379904, 94931877133, ... (that is 1^0, 3^1, 4^2, 5^3, 8^4, 12^5, 22^6, 37^7, ...). In general those powers could be described as (A051920(n)+1)^n for n >= 0. Another property of the palindromes discussed above is that their digits/letters sum to 2^n.
Also (as noted by Robert Munafo) the terms of this sequence are a(n) = (A001405(n)+2)^n for n>=0.
