The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A229677 a(n) = Sum_{k = 0..n} Product_{j = 0..9} C(n+j*k,k). 3
 1, 3628801, 2375880907276801, 4386797386179342934060801, 12868640117405297821759744777996801, 49120459033702373637913562847507823210617601, 222254155614179529476178258638452174287098861960755201, 1132660294172702489573582429384603543633942385302181948349459201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of lattice paths from {n}^10 to {0}^10 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+9*k; n-k, {k}^10). G.f.: Sum_{k >= 0} (10*k)!/k!^10 * x^k / (1-x)^(10*k+1). exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 1814401*x^2 + 791960304240001*x^3 + 1096699347338442061435201*x^4 + ... appears to have integer coefficients. - Peter Bala, Jan 13 2016 MAPLE with(combinat): a:= n-> add(multinomial(n+9*k, n-k, k\$10), k=0..n): seq(a(n), n=0..10); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[multinomial[n + 9*k, Join[{n - k}, Array[k&, 10]]], {k, 0, n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 27 2013, translated from Maple *) CROSSREFS Column k = 10 of A229142. Sequence in context: A181726 A195394 A053501 * A350335 A253992 A253999 Adjacent sequences: A229674 A229675 A229676 * A229678 A229679 A229680 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Sep 27 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)