A194083 Expansion of Sum_{n>=0} x^(n*(n+1)/2) * Product_{k=0..n} (1 + x^(k+1)).

1, 2, 1, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 4, 3, 5, 5, 4, 5, 5, 6, 7, 7, 6, 8, 8, 8, 9, 10, 10, 11, 12, 11, 13, 13, 14, 16, 16, 16, 18, 18, 19, 21, 22, 22, 24, 26, 25, 28, 29, 30, 32, 33, 34, 37, 39, 40, 42, 44, 45, 48, 50, 51, 55, 57, 59, 63, 65, 66, 71, 73, 76, 80, 83, 85, 90, 94, 96, 102, 105, 109, 115, 118, 122, 128, 133, 137, 143, 149, 153, 161, 167, 172, 179, 186, 191, 200

Offset

0,2

Comments

Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=0..n} (1 + x^(k+1)) = 1.

What does this sequence count?

Links

Table of n, a(n) for n=0..96.

Prog

(PARI) N=66; x='x + O('x^N); s =sum(n=0, N, x^(n*(n+1)/2) * prod(k=0, n, 1+x^(k+1) ) ); v=Vec(s)

Crossrefs

Sequence in context: A286326 A097368 A271900 * A109699 A301563 A330896

Adjacent sequences: A194080 A194081 A194082 * A194084 A194085 A194086

Keyword

nonn

Author

Joerg Arndt, Aug 14 2011

Status

approved