login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A063417 Ninth column (k=8) of septinomial array A063265. 4
5, 36, 149, 470, 1251, 2954, 6371, 12789, 24210, 43637, 75438, 125801, 203294, 319545, 490058, 735182, 1081251, 1561914, 2219675, 3107664, 4291661, 5852396, 7888149, 10517675, 13883480, 18155475, 23535036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

FORMULA

a(n) = A063265(n+2,8) = (n+1)*(n+2)*(n^6 +41*n^5 +701*n^4 +6439*n^3 +33930*n^2 +100008*n +100800)/8!.

G.f.: (5-9*x+5*x^2+5*x^3-9*x^4+5*x^5-x^6)/(1-x)^9; the numerator polynomial is N6(8,x) from row n=8 of array A063266.

a(n) = 5*C(n+2,2) + 21*C(n+2,3) + 35*C(n+2,4) + 35*C(n+2,5) + 21*C(n+2,6) + 7*C(n+2,7) + C(n+2,8) (see comment in A213889). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012

a(0)=5, a(1)=36, a(2)=149, a(3)=470, a(4)=1251, a(5)=2954, a(6)=6371, a(7)=12789, a(8)=24210, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Aug 22 2012

MATHEMATICA

Table[Total[Table[Binomial[n+2, i], {i, 2, 8}]{5, 21, 35, 35, 21, 7, 1}], {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {5, 36, 149, 470, 1251, 2954, 6371, 12789, 24210}, 30] (* Harvey P. Dale, Aug 22 2012 *)

CROSSREFS

Cf. A063267.

Sequence in context: A027765 A196481 A096945 * A109726 A272561 A266097

Adjacent sequences:  A063414 A063415 A063416 * A063418 A063419 A063420

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 24 2001

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 08:12 EST 2021. Contains 349401 sequences. (Running on oeis4.)