A053110 Expansion of (-1 + 1/(1-7*x)^7)/(49*x); related to A036226.

1, 28, 588, 10290, 158466, 2218524, 28840812, 353299947, 4121832715, 46164526408, 499416240232, 5243870522436, 53648829191076, 536488291910760, 5257585260725448, 50604258134482437, 479252091744216021

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (49,-1029,12005,-84035,352947,-823543,823543).

Formula

a(n) = 7^(n-1)*binomial(n+7, 6);

G.f.: (-1 + (1-7*x)^(-7))/(x*7^2).

Mathematica

CoefficientList[Series[(-1+1/(1-7x)^7)/(49x), {x, 0, 30}], x] (* or *) LinearRecurrence[{49, -1029, 12005, -84035, 352947, -823543, 823543}, {1, 28, 588, 10290, 158466, 2218524, 28840812}, 30] (* Harvey P. Dale, Jun 03 2015 *)
Table[7^(n-1)*Binomial[n+7, 6], {n, 0, 30}] (* G. C. Greubel, Aug 16 2018 *)

Prog

(Sage)[lucas_number2(n, 7, 0)*binomial(n, 6)/7^8 for n in range(7, 24)] # Zerinvary Lajos, Mar 13 2009
(PARI) vector(30, n, n--; 7^(n-1)*binomial(n+7, 6)) \\ G. C. Greubel, Aug 16 2018
(Magma) [7^(n-1)*Binomial(n+7, 6): n in [0..30]]; // G. C. Greubel, Aug 16 2018

Crossrefs

Cf. A036226, A001792, A036083, A036224.

Sequence in context: A281125 A234618 A107397 * A264459 A004371 A283096

Adjacent sequences: A053107 A053108 A053109 * A053111 A053112 A053113

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved