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A056198
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Defined by Product 1/(1-x^k)^a_k, k=1..inf = 1+x+2*Sum(a_k*x^k, k=2..inf).
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1
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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
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OFFSET
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1,2
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COMMENTS
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Klein and Shadmi call these "Organic Numbers".
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LINKS
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Table of n, a(n) for n=1..26.
Gan Adam, One Mathematics
Moshe Klein and Doron Shadmi, Organic Mathematics
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MAPLE
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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];
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CROSSREFS
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Recurrence suggested by that for A000669.
Sequence in context: A299705 A318231 A242271 * A143742 A038523 A096237
Adjacent sequences: A056195 A056196 A056197 * A056199 A056200 A056201
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Aug 05 2000
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EXTENSIONS
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Antti Karttunen discovered that the Klein-Shadmi "Organic Numbers" are the same as this sequence. - N. J. A. Sloane, Apr 02 2011
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STATUS
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approved
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