A110323 Diagonal sums of a number triangle related to the Jacobsthal numbers.

1, 1, 7, 32, 283, 2643, 32317, 443824, 7115461, 127222805, 2541399091, 55739417376, 1335729425647, 34666455314407, 969419191792633, 29046504524166368, 928541094344685577, 31540972026299055849

Offset: 0

Author

Paul Barry, Jul 20 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A110321.

Programs

Mathematica

J[n_] := (2^n-(-1)^n)/3; a[n_] := Sum[(n-k)!*J[n-2*k+1]/k!, {k, 0, n/2}]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Oct 08 2016 *)

Formula

a(n)=sum{k=0..floor(n/2), (n-k)!*J(n-2k+1)/k!}, J(n)=A001045(n).