login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084901 a(n) = 4^(n-2)*n*(5*n+3)/2. 5
0, 1, 13, 108, 736, 4480, 25344, 136192, 704512, 3538944, 17367040, 83623936, 396361728, 1853882368, 8573157376, 39258685440, 178241142784, 803158884352, 3594887626752, 15994458210304, 70781061038080, 311711546474496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A084900. Third binomial transform of heptagonal numbers A000566. Fourth binomial transform of (0,1,5,0,0,0,...).

Coefficients in the hypergeometric series identity 1 - 13*x/(x + 12) + 108*x*(x - 1)/((x + 12)*(x + 16)) - 736*x*(x - 1)*(x - 2)/((x + 12)*(x + 16)*(x + 20)) + ... = 0, valid in the half-plane Re(x) > 0. Cf. A276289 and A077616. - Peter Bala, May 30 2019

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

FORMULA

G.f.: x*(1+x)/(1-4*x)^3.

E.g.f.: x*(2 + 5*x)*exp(4*x)/2. - G. C. Greubel, Jun 06 2019

MATHEMATICA

Table[2^(2*n-5)*n*(5*n+3), {n, 0, 30}] (* G. C. Greubel, Jun 06 2019 *)

PROG

(PARI) vector(30, n, n--; 2^(2*n-5)*n*(5*n+3)) \\ G. C. Greubel, Jun 06 2019

(MAGMA) [2^(2*n-5)*n*(5*n+3): n in [0..30]]; // G. C. Greubel, Jun 06 2019

(Sage) [2^(2*n-5)*n*(5*n+3) for n in (0..30)] # G. C. Greubel, Jun 06 2019

(GAP) List([0..30], n-> 2^(2*n-5)*n*(5*n+3)) # G. C. Greubel, Jun 06 2019

CROSSREFS

Cf. A084902, A077616, A276289.

Sequence in context: A244176 A038384 A038385 * A006239 A271560 A142040

Adjacent sequences:  A084898 A084899 A084900 * A084902 A084903 A084904

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 10 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)