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A252866
Number T(n,k) of parts p in all partitions of n with largest integer power k (such that A052409(p)=k); triangle T(n,k), n>=1, 0<=k<=A000523(n), read by rows.
1
1, 2, 1, 4, 2, 7, 4, 1, 12, 7, 1, 19, 14, 2, 30, 21, 3, 45, 34, 6, 1, 67, 51, 9, 1, 97, 79, 14, 2, 139, 113, 20, 3, 195, 168, 31, 5, 272, 234, 43, 7, 373, 334, 62, 11, 508, 460, 85, 15, 684, 635, 120, 23, 1, 915, 857, 161, 31, 1, 1212, 1165, 221, 44, 2, 1597
OFFSET
1,2
LINKS
FORMULA
T(2^k,k) = 1.
EXAMPLE
Triangle T(n,k) begins:
01: 1;
02: 2, 1;
03: 4, 2;
04: 7, 4, 1;
05: 12, 7, 1;
06: 19, 14, 2;
07: 30, 21, 3;
08: 45, 34, 6, 1;
09: 67, 51, 9, 1;
10: 97, 79, 14, 2;
11: 139, 113, 20, 3;
12: 195, 168, 31, 5;
13: 272, 234, 43, 7;
14: 373, 334, 62, 11;
15: 508, 460, 85, 15;
16: 684, 635, 120, 23, 1;
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((p-> p+[0, p[1]*j*x^igcd(seq(h[2], h=ifactors(i)[2]))]
)(b(n-i*j, i-1)), j=0..n/i)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)[2]):
seq(T(n), n=1..25);
CROSSREFS
Column k=0 gives A000070(n-1).
Row sums give: A006128.
Sequence in context: A376318 A256610 A276055 * A008796 A254594 A280948
KEYWORD
nonn,tabf,look
AUTHOR
Alois P. Heinz, Dec 23 2014
STATUS
approved