A027473 Second column of A027466.

1, 14, 147, 1372, 12005, 100842, 823543, 6588344, 51883209, 403536070, 3107227739, 23727920916, 179936733613, 1356446145698, 10173346092735, 75960984159088, 564959819683217, 4187349251769726, 30939858360298531, 227977903707462860, 1675637592249852021, 12288009009832248154

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300
• Frank Ellermann, Illustration of binomial transforms.
• Index entries for linear recurrences with constant coefficients, signature (14,-49).

Crossrefs

Cf. A001787, A003415, A053464, A053469.

Programs

Magma

[n*7^(n-1): n in [1..35]]; // Vincenzo Librandi, Jun 06 2011

Mathematica

Join[{a=1,b=14},Table[c=14*b-49*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14,-49},{1, 14},19] (* Stefano Spezia, May 05 2024 *)

Formula

a(n) = n*7^(n-1).

a(n) = 14*a(n-1) - 49*a(n-2) with a(1) = 1, a(2) = 14.

a(n) = A003415(7^n). - Bruno Berselli, Oct 22 2013

From Amiram Eldar, Oct 28 2020: (Start)

Sum_{n>=1} 1/a(n) = 7*log(7/6).

Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(8/7). (End)

From Stefano Spezia, May 05 2024: (Start)

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

E.g.f.: x*exp(7*x). (End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001

Offset changed from 2 to 1 by Vincenzo Librandi, Jun 06 2011