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A250287 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 10).

%I A250287 #11 Sep 03 2021 01:59:14
%S A250287 1,1,1,1,1,1,1,1,1,1,1,10,65,285,1000,3002,8007,19447,43757,92377,
%T A250287 184755,3527140,42031760,326057040,1961245375,9812764391,42530831916,
%U A250287 164059546366,574224816166,1850302218766,5550936701311,156435448534980,2711548312208295
%N A250287 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 10).
%H A250287 Alois P. Heinz, <a href="/A250287/b250287.txt">Table of n, a(n) for n = 0..500</a>
%p A250287 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250287      `if`(t=0, add(b(u-j, o+j-1, irem(t+1, 10)), j=1..u),
%p A250287                add(b(u+j-1, o-j, irem(t+1, 10)), j=1..o)))
%p A250287     end:
%p A250287 a:= n-> b(n, 0$2):
%p A250287 seq(a(n), n=0..35);
%t A250287 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 A250287 Row n=10 of A181937.
%K A250287 nonn
%O A250287 0,12
%A A250287 _Alois P. Heinz_, Nov 16 2014