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

1,6

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..300

Formula

a(n) ~ n! / n^3. - Vaclav Kotesovec, Nov 23 2014

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 *)

Prog

(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)!)))

Crossrefs

Cf. A002630 (permutations with two 3-sequences).

Sequence in context: A357845 A199412 A074613 * A039632 A143816 A220783

Adjacent sequences: A247106 A247107 A247108 * A247110 A247111 A247112

Keyword

nonn

Author

Tani Akinari, Nov 21 2014

Status

approved