A120409 a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6/(1!*2!*3!*4!*5!*6!).

162000, 26471025, 1376829440, 36294822144, 600112800000, 7031325609000, 63117561830400, 457937132487120, 2790771598030416, 14702257341646875, 68449036271616000, 286552568263270400, 1093771338292039680, 3849852478998931776, 12612749124441600000

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (22,-231,1540,-7315,26334,-74613,170544,-319770,497420,-646646, 705432,-646646,497420,-319770,170544,-74613,26334,-7315,1540,-231,22,-1).

Formula

Sum_{n>=1} 1/a(n) = 789878089*Pi^2/18000 + 64687*Pi^4)/150 - 16*Pi^6)/21 + 6603436*zeta(3)/25 + 80136*zeta(5) - 56698539425671/64800000. - Amiram Eldar, Sep 08 2022

Maple

[seq(n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6/(1!*2!*3!*4!*5!*6!), n=1..27)];

Mathematica

Table[(Times@@Table[(n+k)^(k+1), {k, 0, 5}])/Times@@(Range[6]!), {n, 15}] (* Harvey P. Dale, Jun 07 2022 *)

Prog

(Sage) [binomial(n, 1)*binomial(n, 3)*binomial(n, 5)*binomial(n, 2)*binomial(n, 4)*binomial(n, 6) for n in range(6, 19)] # Zerinvary Lajos, May 17 2009

Crossrefs

Cf. A090447, A090448, A090449.

Sequence in context: A184474 A114669 A204306 * A253466 A225811 A244348

Adjacent sequences: A120406 A120407 A120408 * A120410 A120411 A120412

Keyword

easy,nonn

Author

Zerinvary Lajos, Jul 05 2006

Extensions

Offset changed from 0 to 1 by Georg Fischer, May 08 2021

Status

approved