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 A104383 Number of distinct partitions of triangular numbers n*(n+1)/2. 6
 1, 1, 2, 4, 10, 27, 76, 222, 668, 2048, 6378, 20132, 64234, 206848, 671418, 2194432, 7215644, 23853318, 79229676, 264288462, 884987529, 2973772212, 10024300890, 33888946600, 114872472064, 390334057172, 1329347719190, 4536808055808, 15513418629884 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals row sums of triangle A104382. Asymptotics: a(n) ~ exp(Pi*sqrt((n^2+n)/6))/(2*6^(1/4))/(n^2+n)^(3/4). 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 G. C. Greubel, Table of n, a(n) for n = 0..1000 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 Limit_{n-->inf} a(n+1)/a(n) = exp(sqrt(Pi^2/6)) = 3.605822247984... a(n) = A000009(A000217(n)). - Alois P. Heinz, Nov 24 2016 MAPLE with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add( `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n) end: a:= n-> b(n*(n+1)/2): seq(a(n), n=0..30); # Alois P. Heinz, Nov 24 2016 MATHEMATICA Join[{1}, PartitionsQ/@Accumulate[Range[30]]] (* Harvey P. Dale, Dec 29 2012 *) PROG (PARI) {a(n)=polcoeff(prod(k=1, n*(n+1)/2, 1+x^k, 1+x*O(x^(n*(n+1)/2))), n*(n+1)/2)} CROSSREFS Cf. A000009, A000217, A066655, A104382. Sequence in context: A216434 A220829 A339838 * A205480 A108523 A157003 Adjacent sequences: A104380 A104381 A104382 * A104384 A104385 A104386 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 04 2005 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Aug 05 2016 STATUS approved

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