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

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A036226, A001792, A036083, A036224.

Programs

Magma

[7^(n-1)*Binomial(n+7, 6): n in [0..30]]; // G. C. Greubel, Aug 16 2018

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 *)

PARI

vector(30,n,n--; 7^(n-1)*binomial(n+7, 6)) \\ G. C. Greubel, Aug 16 2018

Sage

[lucas_number2(n, 7, 0)*binomial(n,6)/7^8 for n in range(7, 24)] # Zerinvary Lajos, Mar 13 2009

Formula

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

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