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A360971

Number of multisets of size n with elements from [n] whose element sum is larger than the product of all elements.

0, 0, 2, 4, 6, 8, 12, 14, 17, 20, 23, 26, 30, 33, 38, 41, 44, 47, 52, 55, 60, 63, 68, 71, 76, 78, 84, 89, 93, 97, 103, 106, 111, 115, 121, 124, 128, 131, 138, 142, 146, 151, 159, 162, 168, 171, 176, 181, 187, 190, 196, 201, 206, 210, 218, 221, 227, 232, 238 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	LINKS	`Alois P. Heinz, Table of n, a(n) for n = 0..400`
	EXAMPLE	`a(2) = 2: [1,1], [1,2].` `a(3) = 4: [1,1,1], [1,1,2], [1,2,2], [1,1,3].` `a(4) = 6: [1,1,1,1], [1,1,1,2], [1,1,2,2], [1,1,1,3], [1,1,2,3], [1,1,1,4].` `a(8) = 17: [1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,2,2], [1,1,1,1,1,2,2,2], [1,1,1,1,1,1,1,3], [1,1,1,1,1,1,2,3], [1,1,1,1,1,1,3,3], [1,1,1,1,1,1,1,4], [1,1,1,1,1,1,2,4], [1,1,1,1,1,1,3,4], [1,1,1,1,1,1,1,5], [1,1,1,1,1,1,2,5], [1,1,1,1,1,1,1,6], [1,1,1,1,1,1,2,6], [1,1,1,1,1,1,1,7], [1,1,1,1,1,1,2,7], [1,1,1,1,1,1,1,8].`
	MAPLE	b:= proc(n, i, s, p) `if`(s+ni<=p, 0, `if`(n=0 or i=1, 1, g(n, i, s, p))) end: `g:= proc(n, i, s, p) option remember; add(b(n-1, j, s+j, pj), j=1..i) end:` `a:= n-> b(n$2, 0, 1):` `seq(a(n), n=0..60);`
	MATHEMATICA	`b[n_, i_, s_, p_] := If[s + ni <= p, 0, If[n == 0 \|\| i == 1, 1, g[n, i, s, p]]];` `g[n_, i_, s_, p_] := g[n, i, s, p] = Sum[b[n-1, j, s+j, pj], {j, 1, i}];` `a[n_] := b[n, n, 0, 1];` `Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 09 2023, after Alois P. Heinz *)`
	CROSSREFS	`Cf. A103586, A360538, A360563.` `Sequence in context: A273131 A372224 A357371 * A249721 A010063 A260652` `Adjacent sequences: A360968 A360969 A360970 * A360972 A360973 A360974`
	KEYWORD	`nonn`
	AUTHOR	`Alois P. Heinz, Feb 27 2023`
	STATUS	`approved`

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)