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 A104382 Triangle, read by rows, where T(n,k) equals number of distinct partitions of triangular number n*(n+1)/2 into k different summands for n>=k>=1. 5
 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 12, 6, 1, 1, 10, 27, 27, 10, 1, 1, 13, 52, 84, 57, 14, 1, 1, 17, 91, 206, 221, 110, 21, 1, 1, 22, 147, 441, 674, 532, 201, 29, 1, 1, 27, 225, 864, 1747, 1945, 1175, 352, 41, 1, 1, 32, 331, 1575, 4033, 5942, 5102, 2462, 598, 55, 1, 1, 38, 469 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Secondary diagonal equals partitions of n - 1 (A000065). Third diagonal is A104384. Third column is A104385. Row sums are A104383 where limit_{n --> inf} A104383(n+1)/A104383(n) = exp(sqrt(Pi^2/6)) = 3.605822247984... REFERENCES Abramowitz, M. and Stegun, I. A. (Editors). "Partitions into Distinct Parts." S24.2.2 in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 9th printing. New York: Dover, pp. 825-826, 1972. LINKS Alois P. Heinz, Rows n = 1..55, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Eric Weisstein's World of Mathematics, Partition Function Q. FORMULA T(n, 1) = T(n, n) = 1. T(n, n-1) = A000065(n). T(n, 2) = [(n*(n+1)/2-1)/2]. From Álvar Ibeas, Jul 23 2020: (Start) T(n, k) = A008284((n-k+1)*(n+k)/2, k). T(n, k) = A026820((n-k)*(n+k+1)/2, k), with A026820(0, k) = 1. (End) EXAMPLE Rows begin: 1; 1, 1; 1, 2, 1; 1, 4, 4, 1; 1, 7, 12, 6, 1; 1, 10, 27, 27, 10, 1; 1, 13, 52, 84, 57, 14, 1; 1, 17, 91, 206, 221, 110, 21, 1; 1, 22, 147, 441, 674, 532, 201, 29, 1; 1, 27, 225, 864, 1747, 1945, 1175, 352, 41, 1; 1, 32, 331, 1575, 4033, 5942, 5102, 2462, 598, 55, 1; ... PROG (PARI) T(n, k)=if(n

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