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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A187010 G.f. satisfies: A(x) = Sum_{n>=0} x^n*g_n(x)^n where g_n(x) = A(x) - x^n*g_n(x)^n for n>=0. 0
 1, 1, 1, 4, 8, 20, 65, 189, 545, 1672, 5234, 16483, 52508, 168948, 547031, 1782892, 5851234, 19308826, 64012154, 213130527, 712361672, 2389177656, 8038552120, 27125159211, 91774118484, 311265968741, 1058099992873, 3604394906225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS EXAMPLE G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 8*x^4 + 20*x^5 + 65*x^6 +... where A(x) = 1 + x*g_1(x) + x^2*g_2(x)^2 + x^3*g_3(x)^3 +... such that g_n(x) = A(x) - x^n*g_n(x)^n for n>=0. The coefficients in the functions g_n(x) for n=0..8 begin: n=0: [0,1,1,4,8,20,65,189,545,1672,5234,16483,52508,168948,...]; n=1: [1,0,1,3,5,15,50,139,406,1266,3968,12515,39993,128955,...]; n=2: [1,1,0,2,7,16,47,143,415,1264,4005,12713,40484,130346,...]; n=3: [1,1,1,3,5,14,49,150,443,1350,4208,13270,42368,136668,...]; n=4: [1,1,1,4,7,16,55,157,450,1412,4436,13987,44817,144544,...]; n=5: [1,1,1,4,8,19,60,174,495,1507,4728,14878,47318,152338,...]; n=6: [1,1,1,4,8,20,64,183,524,1598,4976,15637,49703,159564,...]; n=7: [1,1,1,4,8,20,65,188,538,1644,5129,16098,51178,164384,...]; n=8: [1,1,1,4,8,20,65,189,544,1664,5198,16339,51954,166940,...]; ... The coefficients in g_n(x)^n for n=0..8 begin: n=0: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]; n=1: [1, 0, 1, 3, 5, 15, 50, 139, 406, 1266, ...]; n=2: [1, 2, 1, 4, 18, 46, 130, 408, 1229, 3770, ...]; n=3: [1, 3, 6, 16, 39, 102, 322, 1026, 3213, 10140, ...]; n=4: [1, 4, 10, 32, 95, 260, 798, 2496, 7691, 24404, ...]; n=5: [1, 5, 15, 50, 165, 506, 1605, 5190, 16610, 53505, ...]; n=6: [1, 6, 21, 74, 258, 846, 2805, 9384, 31068, 102916, ...]; n=7: [1, 7, 28, 105, 385, 1330, 4564, 15723, 53606, 182000,...]; n=8: [1, 8, 36, 144, 554, 2008, 7128, 25208, 88171, 306144,...]; ... where the antidiagonal sums of the above table equals this sequence. Note how g_n(x) satisfies: A(x) = g_n(x) + x^n*g_n(x)^n for n>=0. PROG (PARI) {a(n)=local(G=1, g=vector(n+1, k, 1+x+x*O(x^n))); for(i=1, n, G=1+sum(m=1, n, x^m*g[m+1]^m); g=vector(n+1, k, G-x^(k-1)*g[k]^(k-1)+x*O(x^n)); ); polcoeff(G, n)} CROSSREFS Sequence in context: A115099 A060919 A009333 * A240149 A086912 A168451 Adjacent sequences:  A187007 A187008 A187009 * A187011 A187012 A187013 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 19 2011 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 November 23 17:41 EST 2020. Contains 338595 sequences. (Running on oeis4.)