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A099242 (6n+5)-th terms of expansion of 1/(1 - x - x^6). 3
1, 7, 34, 153, 686, 3088, 13917, 62721, 282646, 1273690, 5739647, 25864698, 116554700, 525233175, 2366870474, 10665883415, 48063918336, 216591552484, 976031547888, 4398313653120, 19820223058176, 89316331907533 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A row of A099239.

Equals INVERT transform of A000389, C(n,5). [Gary W. Adamson, Feb 02 2009]

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-15,20,-15,6,-1).

FORMULA

G.f.: 1/((1-x)^6-x).

a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

a(n) = Sum_{k=0..n} binomial(6*n-5*(k-1), k).

a(n) = Sum_{k=0..n} binomial(n+5*(k+1), k+5*(k+1).

a(n) = Sum_{k=0..n} binomial(n+5*(k+1), n-k).

MATHEMATICA

CoefficientList[Series[1/((1 - x)^6 - x), {x, 0, 50}], x] (* G. C. Greubel, Nov 24 2017 *)

LinearRecurrence[{7, -15, 20, -15, 6, -1}, {1, 7, 34, 153, 686, 3088}, 30] (* Harvey P. Dale, May 06 2018 *)

PROG

(PARI) x='x+O('x^50); Vec(1/((1-x)^6-x)) \\ G. C. Greubel, Nov 24 2017

CROSSREFS

Cf. A000389.

Sequence in context: A080960 A243414 A213119 * A032206 A124466 A055271

Adjacent sequences:  A099239 A099240 A099241 * A099243 A099244 A099245

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified November 20 22:59 EST 2018. Contains 317427 sequences. (Running on oeis4.)