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A061396
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Number of "rooted index-functional forests" (Riffs) on n nodes. Number of "rooted odd trees with only exponent symmetries" (Rotes) on 2n+1 nodes.
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35
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1, 1, 2, 6, 20, 73, 281, 1124, 4618, 19387, 82765, 358245, 1568458, 6933765, 30907194, 138760603, 626898401, 2847946941, 13001772692, 59618918444, 274463781371, 1268064807409, 5877758070220, 27325789128330, 127384553264327, 595318139942874, 2788598203340643, 13090395266913748, 61571972632103632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| J. Awbrey, personal journal, circa 1978. Letter to N. J. A. Sloane, 1980-Aug-04.
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LINKS
| V. Jovovic, Table of n, a(n) for n=0..100
J. Awbrey, Illustration of initial terms
V. Jovovic, First 100 terms
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FORMULA
| G.f. A(x) = 1 + x + 2*x^2 + 6*x^3 + ... satisfies A(x) = Product_{j = 0 to infinity} (1 + x^(j+1)*A(x))^a_j.
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EXAMPLE
| These structures come from recursive primes' factorizations of natural numbers, where the recursion proceeds on both the exponents (^k) and the indices (_k) of the primes invoked in the factorization:
2 = (prime_1)^1 = (p_1)^1, briefly, p, weight of 1 node => a(1) = 1.
3 = (prime_2)^1 = (p_2)^1, briefly, p_p, weight of 2 nodes and
4 = (prime_1)^2 = (p_1)^2, briefly, p^p, weight of 2 nodes => a(2) = 2.
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MAPLE
| a(0) := 1: for k from 1 to 30 do A := add(a(i)*x^i, i=0..k): B := mul((1+x^(j+1)*A)^a(j), j=0..k-1): a(k) := coeff(series(B, x, k+1), x, k): printf(`%d, `, a(k)); od:
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CROSSREFS
| Cf. A062504, A062860.
Sequence in context: A150139 A052884 A150140 * A192497 A104632 A194956
Adjacent sequences: A061393 A061394 A061395 * A061397 A061398 A061399
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KEYWORD
| nice,nonn,easy
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AUTHOR
| Jon Awbrey (jawbrey(AT)oakland.edu), Jun 09 2001
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EXTENSIONS
| Corrected and extended with Maple program by Vladeta Jovovic and David W. Wilson (davidwwilson(AT)comcast.net), Jun 20 2001
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