A294054 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals five.

15, 129, 836, 4789, 25430, 128360, 625905, 2976800, 13896153, 63950894, 291050996, 1312981604, 5881158250, 26191105884, 116085151862, 512487018089, 2255036961813, 9895020092839, 43316960894877, 189247864529166, 825397574526671, 3594688070523059, 15635607417594050

Offset: 6

Author

Alois P. Heinz, Oct 22 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000
• Index entries for linear recurrences with constant coefficients, signature (11, -40, 49, -8, 14, 94, -354, 92, 41, 464, -113, -280, -39, -164, 217, 104, -48, -16, -32, 6, 5, 2, 1, -1)

Crossrefs

Column k=5 of A287213.

Cf. A287276, A287277.

Formula

G.f.: (x^15-3*x^13-2*x^12-4*x^11+7*x^10+21*x^9+9*x^8-33*x^7-44*x^6+48*x^5-10*x^4 +18*x^3+17*x^2-36*x+15)*x^6 / ((x^8-x^7-7*x^5+7*x^4+x^3+4*x^2-5*x+1) *(x^10-x^9 -x^7 -9*x^6 +10*x^5+9*x^4-7*x^3+4*x^2-5*x+1)*(x^6+x^5-x^4-3*x^2-x+1)).

a(n) = A287277(n) - A287276(n).