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 A329323 Triangle read by rows: T(n,k) is the sum of the parts congruent to 0 mod k in the partitions of n into equal parts, 1 <= k <= n. 2
 1, 4, 2, 6, 0, 3, 12, 8, 0, 4, 10, 0, 0, 0, 5, 24, 12, 12, 0, 0, 6, 14, 0, 0, 0, 0, 0, 7, 32, 24, 0, 16, 0, 0, 0, 8, 27, 0, 18, 0, 0, 0, 0, 0, 9, 40, 20, 0, 0, 20, 0, 0, 0, 0, 10, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 72, 48, 36, 24, 0, 24, 0, 0, 0, 0, 0, 12, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 56, 28, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column k lists the terms of A038040 multiplied by k and interspersed with (k-1) zeros. LINKS Table of n, a(n) for n=1..95. FORMULA T(n,k) = A126988(n,k)*A134577(n,k). EXAMPLE Triangle begins: 1; 4, 2; 6, 0, 3; 12, 8, 0, 4; 10, 0, 0, 0, 5; 24, 12, 12, 0, 0, 6; 14, 0, 0, 0, 0, 0, 7; 32, 24, 0, 16, 0, 0, 0, 8; 27, 0, 18, 0, 0, 0, 0, 0, 9; 40, 20, 0, 0, 20, 0, 0, 0, 0, 10; 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11; 72, 48, 36, 24, 0, 24, 0, 0, 0, 0, 0, 12; 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13; 56, 28, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 14; 60, 0, 30, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15; 80, 64, 0, 48, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 16; ... For n = 6 the partitions of 6 into equal parts are [6], [3, 3], [2, 2, 2], [1, 1, 1, 1, 1, 1]. Then, for k = 2 the sum of the parts that are multiples of 2 is 6 + 2 + 2 + 2 = 12, so T(6,2) = 12. CROSSREFS Column 1 is A038040. Row sums give A034718. Leading diagonal gives A000027. The number of positive terms in row n is A000005(n). Cf. A126988, A130540, A134577, A244051. Sequence in context: A019170 A107504 A141674 * A178394 A266391 A091664 Adjacent sequences: A329320 A329321 A329322 * A329324 A329325 A329326 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Nov 21 2019 STATUS approved

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Last modified May 31 17:17 EDT 2023. Contains 363068 sequences. (Running on oeis4.)