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A053110 Expansion of (-1 + 1/(1-7*x)^7)/(49*x); related to A036226. 4
1, 28, 588, 10290, 158466, 2218524, 28840812, 353299947, 4121832715, 46164526408, 499416240232, 5243870522436, 53648829191076, 536488291910760, 5257585260725448, 50604258134482437, 479252091744216021 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified December 10 14:27 EST 2019. Contains 329896 sequences. (Running on oeis4.)