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 A172396 G.f. satisfies: A(x) = G(x/A(x)) where o.g.f. G(x) = A(x*G(x)) = Sum_{n>=0} A003701(n)*x^n. 0
 1, 1, 1, 0, 3, 0, 38, 0, 947, 0, 37394, 0, 2120190, 0, 162980012, 0, 16330173251, 0, 2070201641498, 0, 324240251016266, 0, 61525045423103316, 0, 13913915097436287598, 0, 3698477457114061621492, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The e.g.f. of A003701 is exp(x)/cos(x) = Sum_{n>=0} A003701(n)*x^n/n!. Compare to A157308 and A157310. LINKS Table of n, a(n) for n=0..27. FORMULA a(n) = |A157308(n)| = |A157310(n)| for n>=0. a(2n) = A158119(n) for n>=0; a(2n-1) = 0 for n>=2, with a(1)=1. G.f. A = A(x) satisfies: A(x) = 1/(1-x/A - (x/A)^2/(1-x/A - 2^2*(x/A)^2/(1-x/A - 3^2*(x/A)^2/(1-x/A - 4^2*(x/A)^2/(1-x/A - 5^2*(x/A)^2/(1-x/A -...)))))), a recursive continued fraction. [From Paul D. Hanna, Jan 05 2012] EXAMPLE G.f.: A(x) = 1 + x + x^2 + 3*x^4 + 38*x^6 + 947*x^8 + 37394*x^10 +... where G(x) = A(x*G(x)) is the o.g.f. of A003701: G(x) = 1 + x + 2*x^2 + 4*x^3 + 12*x^4 + 36*x^5 + 152*x^6 + 624*x^7 +... while the e.g.f. of A003701 is given by: exp(x)/cos(x) = 1 + x + 2*x^2/2! + 4*x^3/3! + 12*x^4/4! + 36*x^5/5! +... PROG (PARI) {a(n)=local(X=x+x*O(x^n), G=sum(m=0, n, m!*polcoeff(exp(X)/cos(X), m)*x^m)+x*O(x^n)); polcoeff(x/serreverse(x*G), n)} CROSSREFS Cf. A003701, A158119, A157308, A157310. Sequence in context: A012775 A157308 A157310 * A164806 A105751 A177698 Adjacent sequences: A172393 A172394 A172395 * A172397 A172398 A172399 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 07 2010 STATUS approved

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Last modified November 30 19:18 EST 2023. Contains 367462 sequences. (Running on oeis4.)