A252866 - OEIS

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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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..2048, flattened

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.

Cf. A000523, A052409.

Sequence in context: A376318 A256610 A276055 * A008796 A254594 A280948

Adjacent sequences: A252863 A252864 A252865 * A252867 A252868 A252869

KEYWORD

nonn,tabf,look

AUTHOR

Alois P. Heinz, Dec 23 2014

STATUS

approved