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A262810 Number of lattice paths from {n}^n to {0}^n using steps that decrement one or more components by one. 3
1, 1, 13, 16081, 5552351121, 1050740615666453461, 179349571255187154941191217629, 41020870889694863957061607086939138327565057, 17469051230066445323872793284679234619523576313653708533767425 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A262809(n,n).
a(n) ~ n^(n^2 - n/2 + 1) / (exp(1/12) * 2^(n + log(2)/24) * Pi^((n-1)/2) * log(2)^(n^2+1)). - Vaclav Kotesovec, Mar 23 2016
EXAMPLE
a(2) = 13: [(2,2),(1,2),(0,2),(0,1),(0,0)], [(2,2),(1,2),(0,1),(0,0)], [(2,2),(1,2),(1,1),(0,1),(0,0)], [(2,2),(1,2),(1,1),(0,0)], [(2,2),(1,2),(1,1),(1,0),(0,0)], [(2,2),(2,1),(1,1),(0,1),(0,0)], [(2,2),(2,1),(1,1),(0,0)], [(2,2),(2,1),(1,1),(1,0),(0,0)], [(2,2),(2,1),(2,0),(0,1),(0,0)], [(2,2),(2,1),(1,0),(0,0)], [(2,2),(1,1),(0,1),(0,0)], [(2,2),(1,1),(0,0)], [(2,2),(1,1),(1,0),(0,0)].
MATHEMATICA
Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, n]^n, {i, 0, j}], {j, 0, n^2}], {n, 1, 10}]}] (* Vaclav Kotesovec, Mar 23 2016 *)
PROG
(PARI) a(n)=sum(j=0, n^2, sum(i=0, j, (-1)^i*binomial(j, i)*binomial(j - i, n)^n)) \\ Charles R Greathouse IV, Jul 29 2016
CROSSREFS
Main diagonal of A262809.
Cf. A316677.
Sequence in context: A176096 A215685 A327585 * A340295 A203514 A098562
KEYWORD
nonn,nice
AUTHOR
Alois P. Heinz, Oct 02 2015
STATUS
approved

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)