The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A172391 G.f. satisfies: A(x) = G(x/A(x))^2 and G(x)^2 = A(x*G(x)^2) where G(x) = Sum_{n>=0} C(2n,n)*C(2n+2,n+1)/(n+2)*x^n is the g.f. of A172392. 2
 1, 8, 12, 0, 28, 0, 264, 0, 3720, 0, 63840, 0, 1232432, 0, 25731216, 0, 568130552, 0, 13081215840, 0, 311178567648, 0, 7597974517056, 0, 189518147463232, 0, 4811962763222784, 0, 124028853694440640, 0, 3238304402221646880, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f.: A(x) = x/Series_Reversion(x*G(x)^2)) where G(x) is the g.f. of A172392(n) = A000108(n+1)*A000984(n). Self-convolution of A172393. EXAMPLE G.f.: A(x) = 1 + 8*x + 12*x^2 + 28*x^4 + 264*x^6 + 3720*x^8 +... where A(x) = G(x/A(x))^2 where G(x) is the g.f. of A172392: G(x) = 1 + 4*x + 30*x^2 + 280*x^3 + 2940*x^4 + 33264*x^5 +...+ A172392(n)*x^n +... G(x) = 1 + 2*2*x + 5*6*x^2 + 14*20*x^3 + 42*70*x^4 + 132*252*x^5 +... PROG (PARI) {a(n)=local(G=sum(m=0, n, binomial(2*m, m)*binomial(2*m+2, m+1)/(m+2)*x^m)+x*O(x^n)); polcoeff(x/serreverse(x*G^2), n)} CROSSREFS Cf. A172392, A172393, variants: A172390, A168357, A168451, A168452. Sequence in context: A140478 A111021 A126814 * A227239 A037449 A070477 Adjacent sequences:  A172388 A172389 A172390 * A172392 A172393 A172394 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 05 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 16 17:26 EST 2021. Contains 340206 sequences. (Running on oeis4.)