A112499 - OEIS

A112499

Fourth column of second-order Eulerian triangle A008517 divided by 4.

6, 111, 1100, 8030, 48950, 265625, 1331540, 6310976, 28719094, 126814819, 547457452, 2323131730, 9729382150, 40335953245, 165915269268, 678306115284, 2759909133030, 11187839886855, 45220188014220, 182359367356230, 734088513869846, 2950950104332001, 11849511321016340, 47540932962238760

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OFFSET

4,1

LINKS

Table of n, a(n) for n=4..27.

Index entries for linear recurrences with constant coefficients, signature (20,-175,882,-2835,6072,-8777,8458,-5204,1848,-288).

FORMULA

G.f.: x^4*(6-9*x-70*x^2+163*x^3-42*x^4-72*x^5)/(Product_{j=1..4} (1-j*x)^(5-j)). See the comment on column g.f.s under A008517.

a(n) = 4*a(n-1) + (n-2)*A112498(n-1), n>4, with a(4)=6.

a(n+4) = 6*b(n)-9*b(n-1)-70*b(n-2)+163*b(n-3)-42*b(n-4)-72*b(n-5), n>=0, with b(n):=A112503(n).

CROSSREFS

Cf. A008517, A112498, A112503.