A101862 a(n) = n*(n+1)*(n+7)*(122+57*n+n^2)/120.

24, 108, 302, 671, 1296, 2275, 3724, 5778, 8592, 12342, 17226, 23465, 31304, 41013, 52888, 67252, 84456, 104880, 128934, 157059, 189728, 227447, 270756, 320230, 376480, 440154, 511938, 592557, 682776, 783401, 895280, 1019304, 1156408, 1307572, 1473822, 1656231

Offset: 1

Author

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004

Keywords

• nonn
• easy

Comments

Partial sums of A101861.

6th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 4: 1,11,11,1: 6th row of the array in the examples of A101860.

Links

• C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A101860, A101861.

Programs

Magma

[n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120 : n in [1..50]]; // Wesley Ivan Hurt, Dec 06 2016

Maple

A101862:=n->n*(n+1)*(n+7)*(122+57*n+n^2)/120: seq(A101862(n), n=1..50); # Wesley Ivan Hurt, Dec 06 2016

Mathematica

Table[n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120, {n, 50}] (* Wesley Ivan Hurt, Dec 06 2016 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{24,108,302,671,1296,2275},50] (* Harvey P. Dale, Oct 15 2020 *)

Formula

G.f.: x*(2-x)*(x^2-12*x+12) / (1-x)^6. - R. J. Mathar, Dec 06 2011

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 6. - Wesley Ivan Hurt, Dec 06 2016