This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300734 G.f. A(x) satisfies: [x^n] A( x/A(x)^(2*n^2) ) = 0 for n>1. 2
 1, 1, 8, 261, 18400, 2383800, 523322208, 179218487938, 89683747547520, 62708998782383118, 59089857758999295000, 72802718522742159383487, 114483047893936622981751744, 225239782463528942954480067562, 545115039824232864946208073815480, 1599336782706815943896682999835671375, 5617211714811070144606976491531059082752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjecture: n^2 divides a(n) for n>=1. LINKS Paul D. Hanna, Table of n, a(n) for n = 0..200 EXAMPLE The table of coefficients in A(x/A(x)^(2*n^2)) begins: n=0: [1, 1, 8, 261, 18400, 2383800, 523322208, 179218487938, ...]; n=1: [1, 1, 6, 216, 16180, 2187188, 493439464, 171718406096, ...]; n=2: [1, 1, 0, 105, 10568, 1672006, 412368512, 150825821184, ...]; n=3: [1, 1, -10, 0, 4228, 1024056, 301838400, 120746446648, ...]; n=4: [1, 1, -24, 21, 0, 439248, 186683808, 86739931322, ...]; n=5: [1, 1, -42, 336, -1500, 0, 84158448, 53438819528, ...]; n=6: [1, 1, -64, 1161, -5240, -403722, 0, 23924633200, ...]; n=7: [1, 1, -90, 2760, -26092, -1014644, -61791496, 0, ...]; n=8: [1, 1, -120, 5445, -94112, -1888744, -72316832, -16993280158, 0, ...]; ... such that the main diagonal consists of all zeros after the initial terms. The values a(n)/n^2 for n>=1 begin: [1, 2, 29, 1150, 95352, 14536728, 3657520162, 1401308555430, 774185170152878, ...]. PROG (PARI) {a(n) = my(A=[1, 1]); for(i=2, n, A=concat(A, 0); A[#A] = -Vec(subst(Ser(A), x, x/Ser(A)^(2*(#A-1)^2)))[#A]); A[n+1]} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A292394. Sequence in context: A230727 A272392 A162083 * A081058 A003386 A299328 Adjacent sequences:  A300731 A300732 A300733 * A300735 A300736 A300737 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 11 2018 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 December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)