A113532 a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6.

1, 28, 769, 7108, 36409, 131836, 380713, 937924, 2054353, 4110364, 7654321, 13446148, 22505929, 36167548, 56137369, 84557956, 124076833, 177920284, 249972193, 344857924, 468033241, 625878268, 825796489, 1076318788

Offset: 0

Author

Jonathan Vos Post, Jan 12 2006

Keywords

• easy
• nonn

Comments

1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7*n^6 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 = (x^8 - 1)/(x-1). a(2) = 1 + 2*2 + 3*2^2 + 4*2^3 + 5*2^4 + 6*2^5 + 7*2^6 = 769 is prime. Other primes begin a(6) = 380713, a(12) = 22505929, a(26) = 2236055953, a(38) = 21562615273, a(44) = 51802781449, a(52) = 140712620569.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000012, A005408, A056109, A056578, A056579.

Programs

Mathematica

Table[1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6, {n,0,50}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 28, 769, 7108, 36409, 131836, 380713}, 50] (* G. C. Greubel, Mar 15 2017 *)

PARI

for(n=0,50, print1(1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6, ", ")) \\ G. C. Greubel, Mar 15 2017

Formula

a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6.

O.g.f.: -12636/(-1+x)^4 -4/(-1+x) -21480/(-1+x)^5 -309/(-1+x)^2 -16920/(-1+x)^6 -3342/(-1+x)^3-5040/(-1+x)^7 . - R. J. Mathar, Feb 26 2008