A247109 Number of permutations of length n with two 4-sequences.
0, 0, 0, 0, 1, 2, 11, 65, 433, 3271, 27741, 261231, 2708064, 30671367, 377034018, 5001404982, 71229862678, 1084282429946, 17571257417630, 302064161086250, 5490937395703435, 105243824522368960, 2121386876912041845, 44863116021267642255, 993272322666679219071, 22977273619066571708457
Offset: 1
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..300
Crossrefs
Cf. A002630 (permutations with two 3-sequences).
Programs
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Mathematica
Table[Sum[(-1)^k * k*(k-1)/2 * Sum[Sum[Binomial[k-1,p] * Binomial[k-p-1,i-2*p] * Binomial[n-2*k+p-1,n-3*k+i-1] * (n-3*k+i)!,{p,0,k-1}],{i,Max[0,3*k-n],2*(k-1)}],{k,2,n-3}],{n,1,20}] (* Vaclav Kotesovec, Nov 23 2014 after Tani Akinari *) -
PARI
a(n)=sum(k=2,n-3,(-1)^k*k*(k-1)/2*sum(i=max(0,3*k-n),2*(k-1),sum(p=0,k-1,binomial(k-1,p)*binomial(k-p-1,i-2*p)*binomial(n-2*k+p-1,n-3*k+i-1)*(n-3*k+i)!)))
Formula
a(n) ~ n! / n^3. - Vaclav Kotesovec, Nov 23 2014