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 A285425 Square array A(n,k), n>=1, k>=0, read by antidiagonals, where column k is the expansion of Sum_{j>=1} (2*j - 1)^k*x^(2*j-1)/(1 - x^(2*j-1)). 2
 1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 10, 1, 2, 1, 1, 28, 1, 6, 2, 1, 1, 82, 1, 26, 4, 2, 1, 1, 244, 1, 126, 10, 8, 1, 1, 1, 730, 1, 626, 28, 50, 1, 3, 1, 1, 2188, 1, 3126, 82, 344, 1, 13, 2, 1, 1, 6562, 1, 15626, 244, 2402, 1, 91, 6, 2, 1, 1, 19684, 1, 78126, 730, 16808, 1, 757, 26, 12, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A(n,k) is the sum of k-th powers of odd divisors of n. LINKS Eric Weisstein's World of Mathematics, Odd Divisor Function FORMULA G.f. of column k: Sum_{j>=1} (2*j - 1)^k*x^(2*j-1)/(1 - x^(2*j-1)). EXAMPLE Square array begins: 1,  1,   1,    1,    1,     1,  ... 1,  1,   1,    1,    1,     1,  ... 2,  4,  10,   28,   82,   244,  ... 1,  1,   1,    1,    1,     1,  ... 2,  6,  26,  126,  626,  3126,  ... 2,  4,  10,   28,   82,   244,  ... MATHEMATICA Table[Function[k, SeriesCoefficient[Sum[(2 i - 1)^k x^(2 i - 1)/(1 - x^(2 i - 1)), {i, 1, n}], {x, 0, n}]][j - n], {j, 0, 12}, {n, 1, j}] // Flatten CROSSREFS Columns k=0-5 give: A001227, A000593, A050999, A051000, A051001, A051002. Cf. A109974, A279394, A292919. Sequence in context: A294580 A294587 A064645 * A008307 A249694 A192005 Adjacent sequences:  A285422 A285423 A285424 * A285426 A285427 A285428 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, May 14 2017 STATUS approved

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Last modified October 22 18:38 EDT 2018. Contains 316500 sequences. (Running on oeis4.)