login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293550 a(n) = Sum_{k=0..n} k^3*binomial(2*n-k,n). 3
0, 1, 11, 69, 354, 1650, 7293, 31213, 130832, 540702, 2212550, 8989090, 36327810, 146228940, 586823265, 2349424125, 9389012160, 37467344310, 149345215290, 594753416790, 2366845396500, 9413555798556, 37423053793026, 148719333293394, 590842248405024, 2346813893147500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Main diagonal of iterated partial sums array of cubes (starting with the first partial sums). For nonnegative integers see A002054, for squares see A265612.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for sequences related to sums of cubes

FORMULA

a(n) = [x^n] x*(1 + 4*x + x^2)/(1 - x)^(n+5).

a(n) = 2^(2*n+1)*n^2*(13*n + 7)*Gamma(n+3/2)/(sqrt(Pi)*Gamma(n+5)).

a(n) ~ 26*4^n/sqrt(Pi*n).

MATHEMATICA

Table[Sum[k^3 Binomial[2 n - k, n], {k, 0, n}], {n, 0, 25}]

Table[SeriesCoefficient[x (1 + 4 x + x^2)/(1 - x)^(n + 5), {x, 0, n}], {n, 0, 25}]

Table[2^(2 n + 1) n^2 (13 n + 7) Gamma[n + 3/2]/(Sqrt[Pi] Gamma[n + 5]), {n, 0, 25}]

CoefficientList[Series[(6 - 6 Sqrt[1 - 4 x] - 36 x + 24 Sqrt[1 - 4 x] x + 55 x^2 - 19 Sqrt[1 - 4 x] x^2 - 15 x^3 + Sqrt[1 - 4 x] x^3)/(2 Sqrt[1 - 4 x] x^4), {x, 0, 25}], x]

CoefficientList[Series[(E^(2 x) (36 - 24 x + 13 x^2) BesselI[0, 2 x])/x^2 + (E^(2 x) (-36 + 24 x - 31 x^2 + 13 x^3) BesselI[1, 2 x])/x^3, {x, 0, 25}], x]* Range[0, 25]!

CROSSREFS

Cf. A000537, A000578, A002054, A024166, A101094, A101097, A101102, A265612, A302352.

Sequence in context: A292490 A169731 A212057 * A182188 A099336 A236320

Adjacent sequences:  A293547 A293548 A293549 * A293551 A293552 A293553

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 11 2017

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 October 18 22:03 EDT 2019. Contains 328211 sequences. (Running on oeis4.)