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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 (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: A074364 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

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Last modified December 11 02:24 EST 2019. Contains 329910 sequences. (Running on oeis4.)