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A115593
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Number of forests of rooted trees with total weight n, where a node at height k has weight 2^k (with root considered to be at height 0).
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0
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1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 13, 17, 22, 29, 38, 50, 64, 82, 107, 136, 175, 224, 288, 363, 465, 587, 748, 942, 1196, 1503, 1902, 2385, 3004, 3765, 4729, 5911, 7406, 9246, 11549, 14395, 17941, 22326, 27767, 34501, 42821, 53134, 65828, 81546, 100871
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The sequence b(2n)=0, b(2n+1)=a(n) is the number of trees of weight n.
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FORMULA
| Euler transform of b(n), where b(2n+1) = a(n) and b(2n) = 0.
Contribution from Paul D. Hanna, Oct 26 2011: (Start)
G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x^(2*n)) * x^n/n ).
G.f. satisfies: A(x)*A(-x) = A(x^2). (End)
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EXAMPLE
| a(3)=2; one forest with 3 single-node trees and one with a single two-node tree (root node has weight 1, other node has weight 2).
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PROG
| (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^(2*m)+x*O(x^n))*x^m/m))); polcoeff(A, n)} /* Paul D. Hanna */
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CROSSREFS
| Cf. A000081.
Sequence in context: A027194 A039883 A024186 * A094860 A065417 A005860
Adjacent sequences: A115590 A115591 A115592 * A115594 A115595 A115596
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KEYWORD
| easy,nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 09 2006
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