A293614 a(n) = (8*n + 18)*Pochhammer(n, 6) / 6!.

0, 26, 238, 1176, 4200, 12180, 30492, 68376, 140712, 270270, 490490, 848848, 1410864, 2264808, 3527160, 5348880, 7922544, 11490402, 16353414, 22881320, 31523800, 42822780, 57425940, 76101480, 99754200, 129442950, 166399506, 212048928, 268031456, 336226000

Offset: 0

Author

Peter Luschny, Oct 13 2017

Keywords

• nonn
• easy
• changed

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Programs

Magma

[(8*n + 18)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/Factorial(6): n in [0..50]]; // G. C. Greubel, Oct 23 2017

Maple

A293614 := n -> (8*n + 18)*pochhammer(n,6)/6!;
seq(A293614(n), n=0..29);

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {0, 26, 238, 1176, 4200, 12180, 30492, 68376}, 40] (* or *) a = 1/360 (1080 #1 + 2946 #1^2 + 3121 #1^3 + 1665 #1^4 + 475 #1^5 + 69 #1^6 + 4 #1^7) &; Table[a[n], {n, 0, 40}]
Table[(8*n + 18)*Pochhammer[n, 6]/6!, {n, 0, 50}] (* G. C. Greubel, Oct 23 2017 *)

PARI

for(n=0,50, print1((8*n + 18)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/6!, ", ")) \\ G. C. Greubel, Oct 23 2017

PARI

concat(0, Vec(2*x*(13 + 15*x) / (1 - x)^8 + O(x^40))) \\ Colin Barker, Jul 29 2019

Formula

From Colin Barker, Jul 29 2019: (Start)

G.f.: 2*x*(13 + 15*x) / (1 - x)^8.

a(n) = (n*(1080 + 2946*n + 3121*n^2 + 1665*n^3 + 475*n^4 + 69*n^5 + 4*n^6)) / 360.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7. (End)

Sum_{n>=1} 1/a(n) = 269216/2079 - 4096*Pi/231 - 8192*log(2)/77. - Amiram Eldar, Aug 31 2025