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A229676 a(n) = Sum_{k = 0..n} Product_{j = 0..8} C(n+j*k,k). 3
1, 362881, 12504639772801, 1080492192338314694401, 140810184334251776225321193601, 23183593018924832394604719137184142081, 4439414110286267003192333763481728593177802241, 944848564471993704169724618186222285154304912036663681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of lattice paths from {n}^9 to {0}^9 using steps that decrement one component or all components by 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

FORMULA

a(n) = Sum_{k = 0..n} multinomial(n+8*k; n-k, {k}^9).

G.f.: Sum_{k >= 0} (9*k)!/k!^9 * x^k / (1-x)^(9*k+1).

exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 181441*x^2 + 4168213439041*x^3 + 270123052269252349441*x^4 + ... appears to have integer coefficients. - Peter Bala, Jan 13 2016

MAPLE

with(combinat):

a:= n-> add(multinomial(n+8*k, n-k, k$9), k=0..n):

seq(a(n), n=0..10);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[multinomial[n + 8*k, Join[{n - k}, Array[k&, 9]]], {k, 0, n}]; Table[a[n], {n, 0, 10}] (* Jean-Fran├žois Alcover, Dec 27 2013, translated from Maple *)

CROSSREFS

Column k = 9 of A229142.

Sequence in context: A071551 A181725 A195393 * A230754 A205043 A234896

Adjacent sequences:  A229673 A229674 A229675 * A229677 A229678 A229679

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Sep 27 2013

STATUS

approved

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)