A366859 - OEIS

%I #5 Nov 12 2023 13:30:25

%S 0,1,3,9,28,95,353,1435,6340,30205,154059,836181,4805816,29125915,

%T 185474289,1237159447,8620179448,62589847993,472554134275,

%U 3702702752513,30057098645316,252375781238167,2188733915100465,19579797280231795,180453411239741852,1711498126672376373

%N Antidiagonal sums of A366858.

%t A366858[n_,k_]:=n! SeriesCoefficient[E^((k-1) x)(k Cosh[Sqrt[k]x]+Sqrt[k]Sinh[Sqrt[k]*x])/k,{x,0,n}]; a[n_]:=Sum[A366858[n-k+1,k],{k,n}]; Array[a,26,0] (* or *)

%t A366858[n_,k_]:=(Sqrt[k]((k+Sqrt[k]-1)^n+(k-Sqrt[k]-1)^n)+(k+Sqrt[k]-1)^n-(k-Sqrt[k]-1)^n)/(2Sqrt[k]); a[n_]:=Sum[A366858[n-k+1,k],{k,n}]; Simplify[Array[a,26,0]]

%Y Cf. A366858.

%K nonn

%O 0,3

%A _Stefano Spezia_, Oct 25 2023