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 A245407 Number of endofunctions on [n] such that no element has a preimage of cardinality three. 2
 1, 1, 4, 24, 208, 2325, 31956, 520723, 9812160, 209843145, 5020469200, 132844628411, 3851705048016, 121428210575581, 4135403154270584, 151297710936948675, 5917989635505922816, 246444213949305536017, 10885732208011517726880, 508350675616737391265563 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = n! * [x^n] (exp(x)-x^3/3!)^n. a(n) ~ c * d^n * n^n / exp(n), where d = 2.52566039645910026750819504865..., c = 1.031458655073968039932844239... . - Vaclav Kotesovec, Jul 24 2014 MAPLE b:= proc(n, i) option remember; `if`(n=0 and i=0, 1, `if`(i<1, 0, add(`if`(j=3, 0, b(n-j, i-1) *binomial(n, j)), j=0..n))) end: a:= n-> b(n\$2): seq(a(n), n=0..25); MATHEMATICA Table[n!*SeriesCoefficient[(E^x-x^3/6)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *) With[{k=3}, Flatten[{1, Table[Sum[Binomial[n, j]*Binomial[n, k*j]*(-1)^j*(n-j)^(n-k*j)*(k*j)!/(k!)^j, {j, 0, n/k}], {n, 1, 20}]}]] (* Vaclav Kotesovec, Jul 24 2014 *) CROSSREFS Column k=3 of A245405. Sequence in context: A241980 A297218 A010039 * A162314 A323869 A112141 Adjacent sequences: A245404 A245405 A245406 * A245408 A245409 A245410 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 21 2014 STATUS approved

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Last modified June 3 04:09 EDT 2023. Contains 363103 sequences. (Running on oeis4.)