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 A211474 Signed partitions of n into n parts in {-n..n}\{0}. 1
 1, 1, 5, 17, 78, 375, 1919, 10144, 55189, 306632, 1734019, 9948977, 57790152, 339241199, 2009749140, 12002162624, 72186635028, 436913179401, 2659435211566, 16270345814930, 100002046716732, 617227859736748, 3824280874554199, 23778486784950053, 148329560863192846 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Zero is not allowed as a part. Signed partitions of n into n parts allowing zero as a part: A211475. LINKS Table of n, a(n) for n=1..25. William J. Keith, A bijective toolkit for signed partitions, Ann. Combinat. 15 (1) (2011) 95-117. EXAMPLE a(3) = 5: (1,1,1), (-1,1,3), (-1,2,2), (-2,2,3}, (-3,3,3). MAPLE b:= proc(h, i, t, n) option remember; `if`(i=0, `if`(h=0, 1, 0), `if`(h<0 or i*n b(n\$4): seq(a(n), n=1..15); # Alois P. Heinz, Apr 12 2012 MATHEMATICA Table[1 + Sum[Sum[(IntegerPartitions[k, {j}, Range[n]] // Length) * (IntegerPartitions[n + k, {n - j}, Range[n]] // Length), {j, 0, n - 2}], {k, 1, n*Floor[(n - 1)/2]}], {n, 14}] (* Second program: *) b[h_, i_, t_, n_] := b[h, i, t, n] = If[i == 0, If[h == 0, 1, 0], If[h < 0 || i*n < h, 0, Sum[b[h+j, i-1, j, n], {j, Range[-n, t]~Complement~{0}}]]]; a[n_] := b[n, n, n, n]; Array[a, 25] (* Jean-François Alcover, May 31 2021, after Alois P. Heinz *) CROSSREFS Cf. A211475. Sequence in context: A330800 A293458 A009234 * A149744 A149745 A149746 Adjacent sequences: A211471 A211472 A211473 * A211475 A211476 A211477 KEYWORD nonn AUTHOR David Scambler, Apr 12 2012 EXTENSIONS More terms from Alois P. Heinz, Apr 12 2012 STATUS approved

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Last modified February 28 22:27 EST 2024. Contains 370400 sequences. (Running on oeis4.)