A318628 Number of 7-member subsets of [7*n] whose elements sum to a multiple of n.

0, 1, 1716, 38760, 296010, 1344904, 4496388, 12271518, 28989675, 61474519, 119877472, 218618940, 377447148, 622614630, 988172374, 1517381580, 2264243157, 3295144749, 4690625500, 6547258432, 8979650478, 12122560170, 16133132940, 21193254160, 27512019711

Offset: 0

Author

Alois P. Heinz, Aug 30 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).

Crossrefs

Row n=7 of A318557.

Formula

G.f.: -x*(7*x^12 +1674*x^11 +28569*x^10 +89050*x^9 +116029*x^8 +117612*x^7 +117655*x^6 +117648*x^5 +115939*x^4 +89170*x^3 +28479*x^2 +1710*x+1) / ((x^6+x^5+x^4+x^3+x^2+x+1) *(x-1)^7).

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) + a(n-7) - 6*a(n-8) + 15*a(n-9) - 20*a(n-10) + 15*a(n-11) - 6*a(n-12) + a(n-13). - Wesley Ivan Hurt, Mar 25 2023