A263069 Number of lattice paths from {n}^9 to {0}^9 using steps that decrement one or more components by one.

1, 7087261, 4659168491711401, 7687300579969605991710001, 19133358944433370977791260580721121, 60169662022264019813634467045726478557798101, 220079308019032269943223432841210561656944209845808241, 894709632166224106718347951886305028154659386016685862593012481

Offset: 0

Author

Alois P. Heinz, Oct 08 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Column k=9 of A262809.

Programs

Mathematica

With[{k = 9}, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, n]^k, {i, 0, j}], {j, 0, k*n}], {n, 0, 10}]] (* Vaclav Kotesovec, Mar 22 2016 *)

Formula

a(n) ~ sqrt(c) * d^n / (Pi*n)^4, where d = 7400694480.0494436216324852038000444393262965328... and c = 0.0365684849906610318536810681059888603001404... . - Vaclav Kotesovec, Mar 23 2016