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A061396 Number of "rooted index-functional forests" (Riffs) on n nodes. Number of "rooted odd trees with only exponent symmetries" (Rotes) on 2n+1 nodes. 35
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; text; internal format)
OFFSET

0,3

REFERENCES

J. Awbrey, personal journal, circa 1978. Letter to N. J. A. Sloane, 1980-Aug-04.

LINKS

V. Jovovic, Table of n, a(n) for n=0..100

J. Awbrey, Illustration of initial terms

J. Awbrey, Riffs and Rotes

V. Jovovic, First 100 terms

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.

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.

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:

CROSSREFS

Cf. A062504, A062860.

Sequence in context: A150139 A052884 A150140 * A230823 A192497 A104632

Adjacent sequences:  A061393 A061394 A061395 * A061397 A061398 A061399

KEYWORD

nice,nonn,easy

AUTHOR

Jon Awbrey, Jun 09 2001

EXTENSIONS

Corrected and extended with Maple program by Vladeta Jovovic and David W. Wilson, Jun 20 2001

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.