A186431 Row sums of A186430.

1, 2, 4, 26, 18, 482, 266, 6050, 3114, 21122, 10730, 22178, 11226, 4455362, 2256338, 343874, 173610, 13643522, 6869842, 690621122, 347772738, 16250361602, 8187307306, 17146915106, 8584448890, 720152334722, 365024665978, 59381983394, 29700003082

Offset: 0

Author

Peter Bala, Feb 21 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A053657, A186430.

Programs

Maple

# A186431, uses program for A053657 written by Peter Luschny:
A053657 := proc(n) local P, p, q, s, r;
P := select(isprime, [$2..n]); r:=1;
for p in P do s := 0; q := p-1;
do if q > (n-1) then break fi;
s := s + iquo(n-1, q); q := q*p; od;
r := r * p^s; od; r end:
# Row sums:
a:= n-> add(A053657(n)/(A053657(k)*A053657(n-k)), k = 0..n):
seq (a(n), n = 0..22);

Mathematica

b[n_] := b[n] = Product[p^Sum[Floor[(n-1)/((p-1) p^k)], {k, 0, n}], {p, Prime[ Range[n]]}];
T[n_, k_] := b[n]/(b[k] b[n-k]);
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jun 26 2019 *)

Formula

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