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A301931 G.f. A(x) satisfies: A(x) = x*(1 + A(x)*A'(x)) / (1 - A(x)*A'(x)). 4
1, 2, 14, 154, 2186, 36930, 712158, 15295602, 360155378, 9196938274, 252714360398, 7428201595178, 232480106673562, 7717715629942274, 270896581615492926, 10025955123898058082, 390290027013023089122, 15945008348985522925890, 682270367930391378957198, 30518971384549282782489786, 1424657384555111198491140138, 69290703924209121823629630018 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Compare to: C(x) = x*(1 + 2*C(x)*C'(x)) / (1 + C(x)*C'(x)) holds when C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108).
LINKS
FORMULA
a(n) ~ c * 2^n * n! * n^2, where c = 0.03425366633935068788883129... - Vaclav Kotesovec, Oct 14 2020
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 14*x^3 + 154*x^4 + 2186*x^5 + 36930*x^6 + 712158*x^7 + 15295602*x^8 + 360155378*x^9 + 9196938274*x^10 + ...
RELATED SERIES.
A(x)*A'(x) = x + 6*x^2 + 64*x^3 + 910*x^4 + 15552*x^5 + 304206*x^6 + 6627840*x^7 + 158162238*x^8 + 4087933120*x^9 + 113539676470*x^10 + ...
PROG
(PARI) {a(n) = my(L=x); for(i=1, n, L = x*(1 + L'*L)/(1 - L'*L +x*O(x^n)) ); polcoeff(L, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A354751 A211398 A219430 * A060193 A222200 A175564
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 28 2018
STATUS
approved

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Last modified June 25 11:18 EDT 2024. Contains 373701 sequences. (Running on oeis4.)