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A340992
a(n) is the (2n)-th term of the n-fold self-convolution of the number of divisors function tau.
2
1, 2, 8, 41, 216, 1172, 6491, 36430, 206472, 1179104, 6774048, 39107400, 226683903, 1318427762, 7690414740, 44970645116, 263545466456, 1547445069318, 9101515979306, 53613206171619, 316243949777696, 1867702439169958, 11042787840419398, 65357054283015120
OFFSET
0,2
LINKS
FORMULA
a(n) = [x^(2n)] (Sum_{j>=1} tau(j)*x^j)^n.
a(n) = A320019(2n,n).
MAPLE
b:= proc(n, k) option remember; `if`(k=0, 1,
`if`(k=1, numtheory[tau](n+1), (q->
add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..23);
MATHEMATICA
T[n_, k_] := T[n, k] = If[k == 0, If[n == 0, 1, 0], If[k == 1, If[n == 0, 0, DivisorSigma[0, n]], With[{q = Quotient[k, 2]}, Sum[T[j, q]*T[n - j, k - q], {j, 0, n}]]]];
a[n_] := T[2n, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Dec 13 2023, after Alois P. Heinz in A320019 *)
CROSSREFS
Sequence in context: A254399 A375445 A337753 * A348474 A060436 A020083
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 01 2021
STATUS
approved