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 A325504 Product of products of parts over all strict integer partitions of n. 12
 1, 1, 2, 6, 12, 120, 1440, 40320, 1209600, 1567641600, 2633637888000, 13905608048640000, 5046067048690483200000, 5289893008483207348224000000, 1266933607446134946465526579200000000, 99304891373531545064656621572980736000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..30 FORMULA A001222(a(n)) = A325515(n). a(n) = A003963(A325506(n)). EXAMPLE The strict partitions of 5 are {(5), (4,1), (3,2)} with product a(5) = 5*4*1*3*2 = 120. The sequence of terms together with their prime indices begins:               1: {}               1: {}               2: {1}               6: {1,2}              12: {1,1,2}             120: {1,1,1,2,3}            1440: {1,1,1,1,1,2,2,3}           40320: {1,1,1,1,1,1,1,2,2,3,4}         1209600: {1,1,1,1,1,1,1,1,2,2,2,3,3,4}      1567641600: {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,4}   2633637888000: {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4} MAPLE a:= n-> mul(i, i=map(x-> x[], select(x->         nops(x)=nops({x[]}), combinat[partition](n)))): seq(a(n), n=0..15);  # Alois P. Heinz, Aug 03 2021 # second Maple program: b:= proc(n, i) option remember; `if`(n=0, [1\$2], `if`(i<1, [0, 1], ((f, g)->      [f[1]+g[1], f[2]*g[2]*i^g[1]])(b(n, i-1), b(n-i, min(n-i, i-1)))))     end: a:= n-> b(n\$2)[2]: seq(a(n), n=0..15);  # Alois P. Heinz, Aug 03 2021 MATHEMATICA Table[Times@@Join@@Select[IntegerPartitions[n], UnsameQ@@#&], {n, 0, 10}] CROSSREFS Cf. A006128, A007870 (non-strict version), A015723, A022629 (sum of products of parts), A066186, A066189, A066633, A246867, A325505, A325506, A325512, A325513, A325515. Sequence in context: A193987 A089423 A062349 * A193619 A290406 A319481 Adjacent sequences:  A325501 A325502 A325503 * A325505 A325506 A325507 KEYWORD nonn AUTHOR Gus Wiseman, May 07 2019 STATUS approved

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Last modified September 24 12:17 EDT 2021. Contains 347642 sequences. (Running on oeis4.)