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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<x>:=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

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)