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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081905 A sequence related to binomial(n+6, 6). 3
 1, 10, 79, 552, 3567, 21810, 127905, 725820, 4009920, 21664000, 114840064, 598865920, 3078537216, 15626600448, 78431059968, 389685706752, 1918516592640, 9367021682688, 45387134009344, 218388081147904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A081904. 3rd binomial transform of binomial(n+6, 6). 4th binomial transform of (1,6,15,20,15,6,1,0,0,0,...). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (28, -336, 2240, -8960, 21504, -28672, 16384). FORMULA a(n) = 4^n*(n^6 + 129*n^5 + 5845*n^4 + 115215*n^3 + 993874*n^2 + 3308616*n + 2949120)/2949120. G.f.: (1-3*x)^6/(1-4*x)^7. a(n) = 28*a(n-1) - 336*a(n-2) + 2240*a(n-3) - 8960*a(n-4) + 21504*a(n-5) - 28672*a(n-6) + 16384*a(n-7); a(0)=1, a(1)=10, a(2)=79, a(3)=552, a(4)=3567, a(5)=21810, a(6)=127905. - Harvey P. Dale, Aug 14 2014 E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(4*x) / 720. - G. C. Greubel, Oct 17 2018 MATHEMATICA CoefficientList[Series[(1-3x)^6/(1-4x)^7, {x, 0, 20}], x] (* or *) LinearRecurrence[{28, -336, 2240, -8960, 21504, -28672, 16384}, {1, 10, 79, 552, 3567, 21810, 127905}, 20] (* Harvey P. Dale, Aug 14 2014 *) PROG (PARI) x='x+O(x^30); Vec((1-3*x)^6/(1-4*x)^7) \\ G. C. Greubel, Oct 17 2018 (Magma) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^6/(1-4*x)^7)); // G. C. Greubel, Oct 17 2018 CROSSREFS Cf. A081906. Sequence in context: A160655 A006469 A288630 * A016138 A006329 A077245 Adjacent sequences: A081902 A081903 A081904 * A081906 A081907 A081908 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 31 2003 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 April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)