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 A274762 Number of sequences with up to n copies each of 1,2,...,n. 5
 1, 2, 19, 5248, 191448941, 1856296498826906, 7843008902239185171370147, 21408941228439913825832318523364743824, 52400635808473472283994952631626957015306076632624953, 152306240915343870544748050434914720360496623911547121447677238156864610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..26 FORMULA a(n) ~ exp(11/12) * n^(n^2 - n/2 + 1) / (2*Pi)^((n-1)/2). - Vaclav Kotesovec, May 24 2020 EXAMPLE a(0) = 1: () = the empty sequence. a(1) = 2: (), 1. a(2) = 19: (), 1, 2, 11, 12, 21, 22, 112, 121, 122, 211, 212, 221, 1122, 1212, 1221, 2112, 2121, 2211. MAPLE b:= proc(n, k, i) option remember; `if`(k=0, 1, `if`(i<1, 0, add(b(n, k-j, i-1)/j!, j=0..min(k, n)))) end: a:= n-> add(b(n, k, n)*k!, k=0..n^2): seq(a(n), n=0..10); MATHEMATICA Table[Sum[k!*SeriesCoefficient[Sum[x^j/j!, {j, 0, n}]^n, {x, 0, k}], {k, 0, n^2}], {n, 0, 10}] (* Vaclav Kotesovec, May 24 2020 *) PROG (PARI) {a(n) = sum(i=0, n^2, i!*polcoef(sum(j=0, n, x^j/j!)^n, i))} \\ Seiichi Manyama, May 19 2019 CROSSREFS Row sums of A234574. Main diagonal of A308292. Cf. A000312, A034841. Sequence in context: A365050 A024229 A094663 * A091688 A306207 A355466 Adjacent sequences: A274759 A274760 A274761 * A274763 A274764 A274765 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 04 2016 STATUS approved

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Last modified August 14 19:51 EDT 2024. Contains 375167 sequences. (Running on oeis4.)