A186431 - OEIS

%I #24 Jun 26 2019 03:33:56

%S 1,2,4,26,18,482,266,6050,3114,21122,10730,22178,11226,4455362,

%T 2256338,343874,173610,13643522,6869842,690621122,347772738,

%U 16250361602,8187307306,17146915106,8584448890,720152334722,365024665978,59381983394,29700003082

%N Row sums of A186430.

%F a(n) = Sum_{k=0..n} A053657(n)/(A053657(k)*A053657(n-k)), with the convention that A053657(0) = 1.

%p # A186431, uses program for A053657 written by Peter Luschny:

%p A053657 := proc(n) local P, p, q, s, r;

%p P := select(isprime, [$2..n]); r:=1;

%p for p in P do s := 0; q := p-1;

%p do if q > (n-1) then break fi;

%p s := s + iquo(n-1, q); q := q*p; od;

%p r := r * p^s; od; r end:

%p # Row sums:

%p a:= n-> add(A053657(n)/(A053657(k)*A053657(n-k)), k = 0..n):

%p seq (a(n), n = 0..22);

%t b[n_] := b[n] = Product[p^Sum[Floor[(n-1)/((p-1) p^k)], {k, 0, n}], {p, Prime[ Range[n]]}];

%t T[n_, k_] := b[n]/(b[k] b[n-k]);

%t a[n_] := Sum[T[n, k], {k, 0, n}];

%t Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Jun 26 2019 *)

%Y Cf. A053657, A186430.

%K nonn,easy

%O 0,2

%A _Peter Bala_, Feb 21 2011