A032794 Positive integers of the form n(n+1)(n+2)(n+3)(n+4)/(n+(n+1)+(n+2)+(n+3)+(n+4)) that are a multiple of n.

8, 36, 224, 756, 1232, 2808, 5544, 7488, 12852, 20672, 25704, 38456, 55440, 65780, 90720, 122148, 140616, 183744, 236096, 266112, 334628, 415584, 461168, 563472, 681912, 747684, 893376, 1059380, 1150560, 1350440, 1575288, 1697696, 1963764, 2259936, 2419992

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,4,-4,0,-6,6,0,4,-4,0,-1,1).

Crossrefs

Cf. A032793, A032795.

Programs

PARI

Vec(4*x*(2 + 7*x + 47*x^2 + 125*x^3 + 91*x^4 + 206*x^5 + 164*x^6 + 52*x^7 + 47*x^8 + 9*x^9) / ((1 - x)^5*(1 + x + x^2)^4) + O(x^40)) \\ Colin Barker, May 30 2019

Formula

From Colin Barker, May 30 2019: (Start)

G.f.: 4*x*(2 + 7*x + 47*x^2 + 125*x^3 + 91*x^4 + 206*x^5 + 164*x^6 + 52*x^7 + 47*x^8 + 9*x^9) / ((1 - x)^5*(1 + x + x^2)^4).

a(n) = a(n-1) + 4*a(n-3) - 4*a(n-4) - 6*a(n-6) + 6*a(n-7) + 4*a(n-9) - 4*a(n-10) - a(n-12) + a(n-13) for n>13.

(End)

Extensions

Edited and offset changed by Alois P. Heinz, May 29 2019