A291988 Expansion of 1/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)*(1-5*x^5)).

1, 1, 3, 6, 14, 25, 50, 84, 165, 280, 503, 826, 1477, 2386, 4067, 6625, 11032, 17605, 29039, 45820, 74708, 117410, 187691, 293155, 467733, 724421, 1140157, 1763581, 2758717, 4238285, 6599926, 10082054, 15609032, 23819315, 36607147, 55644926, 85380815, 129185681

Offset: 0

Author

Seiichi Manyama, Sep 07 2017

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..6267
• Index entries for linear recurrences with constant coefficients, signature (1,2,1,1,-5,-7,-14,7,19,26,10,20,-60,-120,120).

Crossrefs

Cf. A291960, A291986, A291987.

Programs

GAP

a:=[1,1,3,6,14,25,50,84,165,280,503,826,1477,2386,4067];;
for n in [16..10^2] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]+a[n-4]-5*a[n-5]-7*a[n-6]-14*a[n-7]+7*a[n-8]+19*a[n-9]+26*a[n-10]+10*a[n-11]+20*a[n-12]-60*a[n-13]-120*a[n-14]+120*a[n-15]; od; a; # Muniru A Asiru, Sep 07 2017

Mathematica

CoefficientList[Series[1/Times@@Table[1-n x^n,{n,5}],{x,0,40}],x] (* or *) LinearRecurrence[{1,2,1,1,-5,-7,-14,7,19,26,10,20,-60,-120,120},{1,1,3,6,14,25,50,84,165,280,503,826,1477,2386,4067},40] (* Harvey P. Dale, Aug 10 2021 *)

PARI

Vec(1/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)*(1-5*x^5)) + O(x^100))

Formula

a(n) = a(n-1) + 2*a(n-2) + a(n-3) + a(n-4) - 5*a(n-5) - 7*a(n-6) - 14*a(n-7) + 7*a(n-8) + 19*a(n-9) + 26*a(n-10) + 10*a(n-11) + 20*a(n-12) - 60*a(n-13) - 120*a(n-14) + 120*a(n-15) for n >= 16. - Muniru A Asiru, Sep 07 2017