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A229675 a(n) = Sum_{k = 0..n} Product_{j = 0..7} C(n+j*k,k). 3
1, 40321, 81730010881, 369400348294790401, 2390471064720364776796801, 18975660656355118819906214670721, 171890067585060168829713844899790066561, 1707759022485971054271963683059722310362986881, 18165821273625565354157327818616137066973745155992321 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of lattice paths from {n}^8 to {0}^8 using steps that decrement one component or all components by 1.
LINKS
FORMULA
a(n) = Sum_{k = 0..n} multinomial(n+7*k; n-k, {k}^8).
G.f.: Sum_{k >= 0} (8*k)!/k!^8 * x^k / (1-x)^(8*k+1).
exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 20161*x^2 + 27243357121*x^3 + 92350114520267521*x^4 + ... appears to have integer coefficients. - Peter Bala, Jan 13 2016
MAPLE
with(combinat):
a:= n-> add(multinomial(n+7*k, n-k, k$8), k=0..n):
seq(a(n), n=0..10);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[multinomial[n + 7*k, Join[{n - k}, Array[k&, 8]]], {k, 0, n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 27 2013, translated from Maple *)
Table[Sum[Product[Binomial[n+j*k, k], {j, 0, 7}], {k, 0, n}], {n, 0, 10}] (* Harvey P. Dale, Aug 25 2014 *)
CROSSREFS
Column k = 8 of A229142.
Sequence in context: A195392 A172632 A255358 * A250905 A250949 A276567
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 27 2013
STATUS
approved

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Last modified July 14 12:56 EDT 2024. Contains 374318 sequences. (Running on oeis4.)