OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..70
J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905
FORMULA
a(n) ~ sqrt(8) * (8^8/7!)^n * n^(7*n) / exp(7*(n+1)). - Vaclav Kotesovec, Mar 03 2016
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!*i7!*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7)!)*(8*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7) - k)/(5040^i1 * 720^i2 * 120^i3 * 24^i4 * 6^i5 * 2^i6), {i7, 0, k - i1 - i2 - i3 - i4 - i5 - i6}], {i6, 0, k - i1 - i2 - i3 - i4 - i5}], {i5, 0, k - i1 - i2 - i3 - i4}], {i4, 0, k - i1 - i2 - i3}], {i3, 0, k - i1 - i2}], {i2, 0, k - i1}], {i1, 0, k}], {k, 0, 10}] (* Vaclav Kotesovec, Mar 02 2016, after Horton and Kurn *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 14 2016
STATUS
approved