A056198 Defined by Product 1/(1-x^k)^a_k, k=1..infinity = 1+x+2*Sum(a_k*x^k, k=2..infinity).

1, 2, 3, 9, 24, 76, 236, 785, 2634, 9106, 31870, 113371, 407438, 1479526, 5415700, 19970119, 74096864, 276466199, 1036598162, 3903844089, 14760093096, 56006631629, 213206289068, 814045174247, 3116569685906, 11961635892951

Offset

1,2

Comments

Klein and Shadmi call these "Organic Numbers".

Links

Table of n, a(n) for n=1..26.

Gan Adam, One Mathematics

Moshe Klein and Doron Shadmi, Organic Mathematics

Maple

a := [1, 2]; for n from 3 to 30 do L := series( mul( (1-x^k)^(-a[k]), k=1..n-1)/(1-x^n)^b, x, n+1); t1 := coeff(L, x, n); R := series( 1+x+2*add(a[k]*x^k, k=2..n-1)+2*b*x^n, x, n+1); t2 := coeff(R, x, n); t3 := solve(t1-t2, b); a := [op(a), t3]; od: A056198 := n->a[n];

Crossrefs

Recurrence suggested by that for A000669.

Sequence in context: A299705 A318231 A242271 * A143742 A038523 A358410

Adjacent sequences: A056195 A056196 A056197 * A056199 A056200 A056201

Keyword

nonn

Author

N. J. A. Sloane, Aug 05 2000

Extensions

Antti Karttunen discovered that the Klein-Shadmi "Organic Numbers" are the same as this sequence. - N. J. A. Sloane, Apr 02 2011

Status

approved