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A052337 Number of partitions into at most a(1) copies of 1, a(2) copies of 2, ... 2
1, 1, 1, 2, 2, 3, 5, 6, 8, 10, 13, 17, 21, 27, 34, 42, 53, 65, 80, 98, 119, 146, 177, 213, 258, 309, 370, 443, 528, 628, 746, 883, 1044, 1231, 1449, 1703, 1997, 2338, 2734, 3190, 3718, 4325, 5025, 5830, 6754, 7816, 9032, 10422, 12016, 13832, 15907, 18274 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f. satisfies A(x) = Product_{i>=1} (1-x^(a(i)*(i+1)))/(1-x^i).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1), j=0..min(n/i, a(i)))))
end:
a:= n-> `if`(n=0, 0, 1)+b(n, n-1):
seq(a(n), n=0..70); # Alois P. Heinz, Jun 12 2018
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1], {j, 0, Min[n/i, a[i]]}]]];
a[n_] := If[n == 0, 0, 1] + b[n, n - 1];
a /@ Range[0, 70] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)
CROSSREFS
Cf. A289501.
Sequence in context: A135279 A035631 A050046 * A308858 A192432 A121081
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Dec 19 1999
STATUS
approved

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Last modified April 22 11:51 EDT 2024. Contains 371898 sequences. (Running on oeis4.)