A112008 Fourth diagonal of second-order Eulerian triangle A008517. Fourth column (m=3) of triangle A112007.

1, 52, 1452, 32120, 644020, 12440064, 238904904, 4642163952, 92199790224, 1883079661824, 39689578055808, 865023253219584, 19515249341231616, 455924361142656000, 11030149104146035200, 276260563641659673600

Offset: 0

Author

Wolfdieter Lang, Sep 12 2005

Keywords

• nonn
• easy

Examples

			1452= a(2) = 9*52 + 3*328.
		

Crossrefs

Cf. A002539 (3rd diagonal of A008517; third column of A112007).

Contribution from Johannes W. Meijer, Oct 16 2009: (Start)

Equals fourth left hand column of A163936.

(End)

Formula

a(n)=A112007(n+3, 3), n>=0.

a(n)= (n+7)*a(n-1) + (n+1)*A002539(n+1), n>=1, a(0)=1.

Contribution from Johannes W. Meijer, Oct 16 2009: (Start)

a(n) = sum((-1)^(n+k)*binomial(2*n+9,k)*stirling1(n-k+8,4-k), k=0..3)

(End)