A016783 a(n) = (3*n+1)^7.

1, 16384, 823543, 10000000, 62748517, 268435456, 893871739, 2494357888, 6103515625, 13492928512, 27512614111, 52523350144, 94931877133, 163840000000, 271818611107, 435817657216, 678223072849, 1028071702528

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The inverse binomial transform is 1, 16383, 790776, 7578522, 27624240, 46539360, 36741600, 11022480, 0, 0,... (0 continued). - R. J. Mathar, May 07 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Crossrefs

Cf. A001015, A016777.

Programs

Magma

[(3*n+1)^7: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

Mathematica

Table[(3n+1)^7,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

Formula

G.f.: (1+16376x+692499x^2+3870352x^3+4890287x^4+1475736x^5+77101x^6 +128x^7)/ (1-x)^8. - R. J. Mathar, May 07 2008

E.g.f.: exp(x)*(2187*x^7+51030*x^6+387828*x^5+1151010*x^4 +1263087*x^3 +395388*x^2 +16383*x+1). - Robert Israel, Jun 15 2016

a(n) = A001015(A016777(n)). - Michel Marcus, Jun 16 2016

Sum_{n>=0} 1/a(n) = (147555*zeta(7) + 28*sqrt(3)*Pi^7)/295245. - Ilya Gutkovskiy, Jun 16 2016