A316081 Sequence shifts left nine places under Weigh transform with a(n) = signum(n) for n<9.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 26, 35, 45, 59, 79, 104, 137, 183, 242, 320, 427, 567, 754, 1008, 1345, 1797, 2409, 3228, 4328, 5817, 7817, 10511, 14154, 19063, 25689, 34655, 46768, 63148, 85336, 115372, 156057, 211233

Offset

0,13

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2500

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 * Product_{n>=1} (1 + x^n)^a(n). - Ilya Gutkovskiy, May 09 2019

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(9):
seq(a(n), n=0..54);

Crossrefs

Column k=9 of A316074.

Cf. A057427, A218026.

Sequence in context: A157046 A017979 A140881 * A238708 A266751 A063827

Adjacent sequences: A316078 A316079 A316080 * A316082 A316083 A316084

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved