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

1,1

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).

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)

Prog

(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

Crossrefs

Cf. A032793, A032795.

Sequence in context: A030112 A001555 A032770 * A000757 A126756 A203297

Adjacent sequences: A032791 A032792 A032793 * A032795 A032796 A032797

Keyword

nonn,easy

Author

Patrick De Geest, May 15 1998

Extensions

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

Status

approved