A248720 a(n) = (n*(n+1))^5.

0, 32, 7776, 248832, 3200000, 24300000, 130691232, 550731776, 1934917632, 5904900000, 16105100000, 40074642432, 92389579776, 199690286432, 408410100000, 796262400000, 1488827973632, 2682916351776, 4678757435232, 7923516800000, 13069123200000

Offset

0,2

Comments

This is the sequence (2^5)*A059860(n)= (2*binomial(n+1,2))^5, n >= 0. - Wolfdieter Lang, Nov 03 2014

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Formula

a(n) = A002378(n)^5.

a(n) = 32*A059860(n) for n>0.

G.f.: 32*x*(x^8 + 232*x^7 + 5158*x^6 + 27664*x^5 + 47290*x^4 + 27664*x^3 + 5158*x^2 + 232*x + 1) / (1 - x)^11 (from A059860).

Sum_{n>=1} 1/a(n) = 126 - 35*Pi^2/3 - Pi^4/9. - Vaclav Kotesovec, Sep 25 2019

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - Wesley Ivan Hurt, Jan 20 2024

Maple

[ seq(n^5*(n+1)^5, n = 0..100) ];

Mathematica

Table[(n (n + 1))^5, {n, 0, 70}] (* or *) CoefficientList[Series[32 x (x^8 + 232 x^7 + 5158 x^6 + 27664 x^5 + 47290 x^4 + 27664 x^3 + 5158 x^2 + 232 x + 1)/(1 - x)^11, {x, 0, 30}], x]
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 32, 7776, 248832, 3200000, 24300000, 130691232, 550731776, 1934917632, 5904900000, 16105100000}, 20] (* Harvey P. Dale, Apr 23 2017 *)

Prog

(Magma) [(n*(n+1))^5: n in [0..30]];

Crossrefs

Cf. A059860, A002378 (n*(n+1)), A035287(n+1) ((n*(n+1))^2), A060459 ((n*(n+1))^3), A248619 ((n*(n+1))^4).

Sequence in context: A224100 A224107 A016829 * A069052 A334604 A342455

Adjacent sequences: A248717 A248718 A248719 * A248721 A248722 A248723

Keyword

nonn,easy

Author

Eugene Chong, Oct 16 2014

Extensions

Terms a(32) and beyond corrected by Andrew Howroyd, Feb 20 2018

Status

approved