The OEIS is supported by the many generous donors to the OEIS Foundation.

 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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242795 a(n) = [x^n] ( 1 + x*A(x)^(n+1) )^(n+1) / (n+1) for n>=0, with a(0)=1. 1
 1, 1, 4, 35, 466, 8072, 168330, 4045603, 109089538, 3242538284, 104946776716, 3665946814257, 137291732981170, 5483948111154008, 232660368810666229, 10447887814670412307, 495139557493903545618, 24699919104193662112382, 1293980412831022073519196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare to the g.f. G(x) = x + x*G(G(x)) of A030266 that satisfies: A030266(n+1) = [x^n] ( 1 + G(x) )^(n+1) / (n+1) for n>=0. LINKS Table of n, a(n) for n=0..18. EXAMPLE G.f.: A(x) = 1 + x + 4*x^2 + 35*x^3 + 466*x^4 + 8072*x^5 + 168330*x^6 +... Form a table of coefficients of x^k in (1 + x*A(x)^(n+1))^(n+1) like so: n=0: [1, 1, 1, 4, 35, 466, 8072, 168330, ...]; n=1: [1, 2, 5, 22, 178, 2228, 37141, 755702, ...]; n=2: [1, 3, 12, 64, 516, 6126, 97725, 1929927, ...]; n=3: [1, 4, 22, 140, 1177, 13548, 206876, 3946612, ...]; n=4: [1, 5, 35, 260, 2330, 26626, 391830, 7202170, ...]; n=5: [1, 6, 51, 434, 4185, 48432, 694714, 12312642, ...]; n=6: [1, 7, 70, 672, 6993, 83174, 1178310, 20224653, ...]; n=7: [1, 8, 92, 984, 11046, 136392, 1932876, 32364824, ...]; n=8: [1, 9, 117, 1380, 16677, 215154, 3084024, 50833962, ...]; n=9: [1, 10, 145, 1870, 24260, 328252, 4801655, 78652350, ...]; ... then this sequence is formed from the main diagonal: [1/1, 2/2, 12/3, 140/4, 2330/5, 48432/6, 1178310/7, 32364824/8, ...]. PROG (PARI) {a(n)=local(A=[1, 1]); for(m=1, n, A=concat(A, 0); A[m+1]=Vec((1+x*Ser(A)^(m+1))^(m+1))[m+1]/(m+1)); A[n+1]} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A242794. Sequence in context: A183878 A132694 A270917 * A349527 A287886 A342207 Adjacent sequences: A242792 A242793 A242794 * A242796 A242797 A242798 KEYWORD nonn AUTHOR Paul D. Hanna, May 22 2014 STATUS approved

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

Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)