login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A271933
G.f. A(x) satisfies: A(x) = A( x^11 + 11*x*A(x)^11 )^(1/11), with A(0)=0, A'(0)=1.
4
1, 1, 6, 46, 391, 3519, 32844, 314364, 3065049, 30309929, 303099290, 3058547381, 31095231708, 318128139796, 3272175152355, 33812476576290, 350804444501589, 3652493334187197, 38148263715573364, 399552867370295155, 4195305107766973240, 44150591852677070280, 465588059585378099226, 4919039064854516328821, 52059830109088065802395, 551834199223958450647359, 5857932269440676202573084
OFFSET
1,3
COMMENTS
Compare the g.f. to the following identities:
(1) C(x) = C( x^2 + 2*x*C(x)^2 )^(1/2),
(2) C(x) = C( x^3 + 3*x*C(x)^3 )^(1/3),
where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108).
More generally, for prime p there exists an integer series G(x) that satisfies: G(x) = G( x^p + p*x*G(x)^p )^(1/p) with G(0)=0, G'(0)=1 (conjecture).
LINKS
EXAMPLE
G.f.: A(x) = x + x^2 + 6*x^3 + 46*x^4 + 391*x^5 + 3519*x^6 + 32844*x^7 + 314364*x^8 + 3065049*x^9 + 30309929*x^10 + 303099290*x^11 + 3058547381*x^12 +...
where A(x)^11 = A( x^11 + 11*x*A(x)^11 ).
RELATED SERIES.
A(x)^11 = x^11 + 11*x^12 + 121*x^13 + 1331*x^14 + 14641*x^15 + 161051*x^16 + 1771561*x^17 + 19487171*x^18 + 214358881*x^19 + 2357947691*x^20 + 25937424601*x^21 + 285311670612*x^22 + 3138428376754*x^23 + 34522712144657*x^24 +...
PROG
(PARI) {a(n) = my(A=x+x^2, X=x+x*O(x^n)); for(i=1, n, A = subst(A, x, x^11 + 11*X*A^11)^(1/11) ); polcoeff(A, n)}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
Sequence in context: A253654 A301421 A288689 * A084772 A199563 A349332
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 16 2016
STATUS
approved