

A193242


a(n) = (C(n, floor(n/2)) + 2)^n for n >= 0.


3



1, 3, 16, 125, 4096, 248832, 113379904, 94931877133, 722204136308736, 9223372036854775808, 1117730665547154976408576, 214633637635011206805784100864, 397495155639882245867698528490622976, 1135797931555041090259334993227408493600768
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


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.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..59


FORMULA

a(n) = (A051920(n) + 1)^n.
a(n) = (A001405(n) + 2)^n.


MATHEMATICA

Table[(Binomial[n, Floor[n/2]] + 2)^n, {n, 0, 20}] (* G. C. Greubel, Feb 20 2017 *)


PROG

(PARI) for(n=0, 20, print1((binomial(n, floor(n/2)) + 2)^n, ", ")) \\ G. C. Greubel, Feb 20 2017


CROSSREFS

Cf. A007318, A051920, A001405.
Sequence in context: A246527 A159594 A246525 * A247591 A188805 A214645
Adjacent sequences: A193239 A193240 A193241 * A193243 A193244 A193245


KEYWORD

nonn


AUTHOR

Alexander R. Povolotsky, Feb 11 2013


EXTENSIONS

Corrected a(8) onward  G. C. Greubel, Feb 20 2017


STATUS

approved



