A123491 Diagonal sums of number triangle A123490.

1, 2, 5, 10, 22, 48, 112, 274, 715, 1982, 5837, 18180, 59644, 205296, 739032, 2775180, 10846965, 44039754, 185391469, 807776198, 3637193474, 16900721824, 80939650552, 399061251246, 2023408865983, 10540656630118

Offset: 0

Author

Paul Barry, Oct 01 2006

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..675

Crossrefs

Cf. A123490.

Programs

Mathematica

Table[Sum[((k + 2)^(n - 2 k) + k)/(k + 1), {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Oct 14 2017 *)

PARI

for(n=0,25, print1(sum(k=0,floor(n/2), ((k + 2)^(n - 2 k) + k)/(k + 1)), ", ")) \\ G. C. Greubel, Oct 14 2017

Formula

a(n) = Sum_{k=0..floor(n/2)} ((k+2)^(n-2k)+k)/(k+1).