

A171634


Number of compositions of n such that the number of parts is divisible by the greatest part.


2



1, 1, 3, 2, 8, 13, 21, 38, 89, 173, 302, 545, 1109, 2309, 4564, 8601, 16188, 31365, 62518, 125813, 251119, 493123, 956437, 1854281, 3633938, 7218166, 14444539, 28868203, 57300450, 112921744, 221760513, 436117749, 861764899, 1711773936
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OFFSET

1,3


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..715 (terms 1..250 from Alois P. Heinz)


FORMULA

G.f.: Sum_{n>=0} Sum_{dn} ((x^(d+1)x)^n(x^dx)^n)/(x1)^n.


MAPLE

b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=0, 1, 0), add(b(ni, t+1, max(i, g)), i=1..n)) end: a:= n> b(n, 0, 0): seq(a(n), n=1..40); # Alois P. Heinz, Dec 15 2009


MATHEMATICA

b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[t, g] == 0, 1, 0], Sum[b[n  i, t + 1, Max[i, g]], {i, 1, n}]];
a[n_] := b[n, 0, 0];
Array[a, 40] (* JeanFrançois Alcover, Nov 11 2020, after Alois P. Heinz *)


CROSSREFS

Cf. A168659, A171632.
Sequence in context: A088551 A301903 A165660 * A107300 A285787 A047946
Adjacent sequences: A171631 A171632 A171633 * A171635 A171636 A171637


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Dec 13 2009


EXTENSIONS

More terms from Alois P. Heinz, Dec 15 2009


STATUS

approved



