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Diagonal sums of number triangle A123490.
2

%I #7 Oct 14 2017 21:27:16

%S 1,2,5,10,22,48,112,274,715,1982,5837,18180,59644,205296,739032,

%T 2775180,10846965,44039754,185391469,807776198,3637193474,16900721824,

%U 80939650552,399061251246,2023408865983,10540656630118

%N Diagonal sums of number triangle A123490.

%H G. C. Greubel, <a href="/A123491/b123491.txt">Table of n, a(n) for n = 0..675</a>

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

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

%o (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

%Y Cf. A123490.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 01 2006