A321634 Number of arrangements of n 1's, n 2's, ..., n n's avoiding equal consecutive terms.

1, 1, 2, 174, 2265024, 7946203275000, 12229789732207993835280, 12202002913678756821228939869239920, 10937192762438008527903830198163831816546577931520, 11655577382287102750765311537460065620507094071664576111302628243840

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..26

Mathematics.StackExchange, Find the number of k 1's, k 2's, ... , k n's - total kn cards, Apr 08 2012.

Formula

a(n) ~ n^(n^2 - n/2 + 1) / ((2*Pi)^((n-1)/2) * exp(n - 5/12)). - Vaclav Kotesovec, Nov 24 2018

Prog

(PARI) {a(n) = sum(i=n, n^2, i!*polcoef(sum(j=1, n, (-1)^(n-j)*binomial(n-1, j-1)*x^j/j!)^n, i))} \\ Seiichi Manyama, May 27 2019

Crossrefs

Cf. A000142, A110706, A114938, A193638, A321633, A321666.

Sequence in context: A360478 A193638 A215123 * A219724 A103427 A216355

Adjacent sequences: A321631 A321632 A321633 * A321635 A321636 A321637

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2018

Status

approved