The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056117 Expansion of (1+8*x)/(1-x)^9. 3
 1, 17, 117, 525, 1815, 5247, 13299, 30459, 64350, 127270, 238238, 425646, 730626, 1211250, 1947690, 3048474, 4657983, 6965343, 10214875, 14718275, 20868705, 29156985, 40190085, 54712125, 73628100, 98030556, 129229452, 168785452 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = (9*n+8)*binomial(n+7, 7)/8. G.f.: (1+8*x)/(1-x)^9. From G. C. Greubel, Jan 18 2020: (Start) a(n) = 9*binomial(n+8,8) - 8*binomial(n+7,7). E.g.f.: (40320 + 645120*x + 1693440*x^2 + 1505280*x^3 + 588000*x^4 + 112896*x^5 + 10976*x^6 + 512*x^7 + 9*x^8)*exp(x)/40320. (End) MAPLE seq( (9*n+8)*binomial(n+7, 7)/8, n=0..30); # G. C. Greubel, Jan 18 2020 MATHEMATICA Table[9*Binomial[n+8, 8] -8*Binomial[n+7, 7], {n, 0, 30}] (* G. C. Greubel, Jan 18 2020 *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 17, 117, 525, 1815, 5247, 13299, 30459, 64350}, 30] (* Harvey P. Dale, Nov 23 2022 *) PROG (PARI) vector(31, n, (9*n-1)*binomial(n+6, 7)/8) \\ G. C. Greubel, Jan 18 2020 (Magma) [(9*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // G. C. Greubel, Jan 18 2020 (Sage) [(9*n+8)*binomial(n+7, 7)/8 for n in (0..30)] # G. C. Greubel, Jan 18 2020 (GAP) List([0..30], n-> (9*n+8)*Binomial(n+7, 7)/8 ); # G. C. Greubel, Jan 18 2020 CROSSREFS Cf. A093644 ((9, 1) Pascal, column m=8). Partial sums of A052206. Sequence in context: A044349 A044730 A086020 * A196575 A003109 A066607 Adjacent sequences: A056114 A056115 A056116 * A056118 A056119 A056120 KEYWORD easy,nonn,changed AUTHOR Barry E. Williams, Jul 04 2000 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 November 27 03:51 EST 2022. Contains 358362 sequences. (Running on oeis4.)