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Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 10).
3

%I #11 Sep 03 2021 01:59:14

%S 1,1,1,1,1,1,1,1,1,1,1,10,65,285,1000,3002,8007,19447,43757,92377,

%T 184755,3527140,42031760,326057040,1961245375,9812764391,42530831916,

%U 164059546366,574224816166,1850302218766,5550936701311,156435448534980,2711548312208295

%N Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 10).

%H Alois P. Heinz, <a href="/A250287/b250287.txt">Table of n, a(n) for n = 0..500</a>

%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1,

%p `if`(t=0, add(b(u-j, o+j-1, irem(t+1, 10)), j=1..u),

%p add(b(u+j-1, o-j, irem(t+1, 10)), j=1..o)))

%p end:

%p a:= n-> b(n, 0$2):

%p seq(a(n), n=0..35);

%t nmax = 30; CoefficientList[Series[1 + Sum[(x^(10 - k) * HypergeometricPFQ[{1}, {11/10 - k/10, 6/5 - k/10, 13/10 - k/10, 7/5 - k/10, 3/2 - k/10, 8/5 - k/10, 17/10 - k/10, 9/5 - k/10, 19/10 - k/10, 2 - k/10}, -x^10/10000000000])/(10 - k)!, {k, 0, 9}] / HypergeometricPFQ[{}, {1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10}, -x^10/10000000000], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 21 2021 *)

%Y Row n=10 of A181937.

%K nonn

%O 0,12

%A _Alois P. Heinz_, Nov 16 2014