A036226 Expansion of 1/(1-7*x)^7.

1, 49, 1372, 28812, 504210, 7764834, 108707676, 1413199788, 17311697403, 201969803035, 2262061793992, 24471395771368, 256949655599364, 2628792630362724, 26287926303627240, 257621677775546952

Offset: 0

Author

Wolfdieter Lang

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n >= 6) of 8 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. - Zerinvary Lajos, Jun 16 2008

Links

• Vincenzo Librandi, 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. A036084.

Programs

Magma

[7^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Maple

seq(binomial(n+6,6)*7^n,n=0..16); # Zerinvary Lajos, Jun 16 2008

Mathematica

CoefficientList[Series[1/(1-7x)^7,{x,0,20}],x] (* or *) LinearRecurrence[ {49,-1029,12005,-84035,352947,-823543,823543},{1,49,1372,28812,504210,7764834,108707676},20] (* Harvey P. Dale, Feb 21 2013 *)

Sage

[lucas_number2(n, 7, 0)*binomial(n,6)/7^6 for n in range(6, 22)] # Zerinvary Lajos, Mar 13 2009

Formula

a(n) = 7^n*binomial(n+6, 6).

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

a(n) = 49*a(n-1) - 1029*a(n-2) + 12005*a(n-3) - 84035*a(n-4) + 352947*a(n-5) - 823543*a(n-6) + 823543*a(n-7), a(0)=1, a(1)=49, a(2)=1372, a(3)=28812, a(4)=504210, a(5)=7764834, a(6)=108707676. - Harvey P. Dale, Feb 21 2013