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A268852 Number of sequences with 9 copies each of 1,2,...,n and longest increasing subsequence of length n. 3
1, 1, 48619, 227749730869, 21364658238692907265, 18683332440278067962764855531, 96042041352156959435669839199503441435, 2124172213523649116114190361767338538457819064671, 161347197004751609388708454579308609212572710243373701247489 (list; graph; refs; listen; history; text; internal format)
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

Row n=9 of A047909.

Sequence in context: A234230 A251597 A228676 * A024753 A024761 A245862

Adjacent sequences:  A268849 A268850 A268851 * A268853 A268854 A268855

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 14 2016

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)