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A186431
Row sums of A186430.
2
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
0,2
FORMULA
a(n) = Sum_{k=0..n} A053657(n)/(A053657(k)*A053657(n-k)), with the convention that A053657(0) = 1.
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 *)
CROSSREFS
Sequence in context: A162118 A128774 A218258 * A129894 A028386 A362001
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Feb 21 2011
STATUS
approved