login
Antidiagonal sums of triangle A121775.
1

%I #8 Aug 15 2023 02:08:50

%S 1,1,3,6,10,16,23,36,52,76,118,181,271,427,675,1057,1686,2705,4318,

%T 6923,11142,17966,28999,46793,75522,122018,197254,318907,515616,

%U 833796,1348542,2181304,3528487,5707947,9234075,14938991,24169111,39103056,63265607,102359886

%N Antidiagonal sums of triangle A121775.

%F a(n) = Sum_{k=0..[n/2]} Sum_{d|(n-k)} phi((n-k)/d)*C(d,k) for n>0, with a(0)=1.

%t a[0] = 1; a[n_] := Sum[DivisorSum[n-k, EulerPhi[(n-k)/#] * Binomial[#, k] &], {k, 0, Floor[n/2]}]; Array[a, 50, 0] (* _Amiram Eldar_, Aug 15 2023 *)

%o (PARI) a(n)=if(n==0,1,sum(k=0,n\2,sumdiv(n-k,d,eulerphi((n-k)/d)*binomial(d,k))))

%Y Cf. A000010, A121775.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 23 2006