OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..65
J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905
FORMULA
a(n) ~ 3 * (9^9/8!)^n * n^(8*n) / exp(8*(n+1)). - Vaclav Kotesovec, Mar 03 2016
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!*i7!*i8!*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8)!)*(9*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*i8 + 9*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*i8 + 9*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8) - k)/(8!^i1 * 7!^i2 * 6!^i3 * 5!^i4 * 4!^i5 * 3!^i6 * 2!^i7), {i8, 0, k - i1 - i2 - i3 - i4 - i5 - i6 - i7}], {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