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A320224 a(1) = 1; a(n > 1) = Sum_{k = 1..n-1} Sum_{d|k, d < k} a(d). 5
1, 0, 1, 2, 3, 4, 6, 7, 10, 12, 16, 17, 25, 26, 33, 38, 48, 49, 65, 66, 84, 92, 109, 110, 142, 146, 172, 184, 219, 220, 274, 275, 323, 341, 390, 400, 484, 485, 551, 578, 669, 670, 792, 793, 904, 952, 1062, 1063, 1243, 1250, 1408, 1458, 1632, 1633, 1870, 1890 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(1) = 1; a(n > 1) = Sum_{d = 1..n-1} a(d) * floor((n-1)/d - 1).

G.f. A(x) satisfies A(x) = x + (x/(1 - x)) * Sum_{k>=2} A(x^k). - Ilya Gutkovskiy, Sep 06 2019

MATHEMATICA

sau[n_]:=If[n==1, 1, Sum[sau[d], {k, n-1}, {d, Most[Divisors[k]]}]];

Table[sau[n], {n, 60}]

PROG

(MAGMA) sol:=[1]; for n in [2..56] do Append(~sol, &+[sol[d]*Floor((n-1)/d-1):d in [1..n-1]]); end for; sol; // Marius A. Burtea, Sep 07 2019

(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=sum(k=1, n-1, v[k]*((n-1)\k - 1))); v} \\ Andrew Howroyd, Sep 07 2019

CROSSREFS

Cf. A002541, A003238, A010766, A014668, A126656, A167865, A316782, A317712, A320222, A320225.

Sequence in context: A051424 A308632 A137606 * A328172 A239468 A119793

Adjacent sequences:  A320221 A320222 A320223 * A320225 A320226 A320227

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 07 2018

STATUS

approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)