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A076112
Triangle (read by rows) in which the n-th row contains first n terms of n geometric progression with first term 1 and common ratio (n-1).
2
1, 1, 2, 1, 3, 9, 1, 4, 16, 64, 1, 5, 25, 125, 625, 1, 6, 36, 216, 1296, 7776, 1, 7, 49, 343, 2401, 16807, 117649, 1, 8, 64, 512, 4096, 32768, 262144, 2097152, 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 1, 10, 100, 1000, 10000, 100000, 1000000
OFFSET
1,3
COMMENTS
Table T(n,k) = (n+k-1)^(n-1) n,k > 0 read by antidiagonals. - Boris Putievskiy, Dec 17 2012
LINKS
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
FORMULA
As a linear array, the sequence is a(n) = A002024(n)^A002260(n) or a(n) = (t+1)^(n-t*(t+1)/2-1), where t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 17 2012
EXAMPLE
Triangle begins:
1;
1,2;
1,3,9;
1,4,16,64;
1,5,25,125,625;
1,6,36,216,1296,7776;
...
MATHEMATICA
Table[n^Range[0, n-1], {n, 10}]//Flatten (* Harvey P. Dale, Jan 27 2020 *)
CROSSREFS
Sequence in context: A236438 A101486 A086606 * A208744 A122454 A189650
KEYWORD
easy,nonn,tabl
AUTHOR
Amarnath Murthy, Oct 09 2002
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003
STATUS
approved