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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108990 Triangle, read by rows, where the g.f. of row n, R_n(x), is a polynomial of degree n that satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1, with R_0(x) = 1. 6
 1, 1, 1, 1, 2, 3, 1, 3, 9, 22, 1, 4, 18, 76, 287, 1, 5, 30, 180, 1025, 5496, 1, 6, 45, 350, 2670, 19656, 139727, 1, 7, 63, 602, 5761, 54096, 495964, 4447234, 1, 8, 84, 952, 10962, 125328, 1411228, 15629720, 170501039, 1, 9, 108, 1416, 19062, 257040 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..50. EXAMPLE The g.f. of row 4 is: 1 + 4*x + 18*x^2 + 76*x^3 + 287*x^4 and equals the initial coefficients from [x^0] to [x^4] in: (1+ x*R_3(x))^4 = (1 + x*(1 + 3*x + 9*x^2 + 22*x^3))^4. Triangle begins: 1; 1, 1; 1, 2, 3; 1, 3, 9, 22; 1, 4, 18, 76, 287; 1, 5, 30, 180, 1025, 5496; 1, 6, 45, 350, 2670, 19656, 139727; 1, 7, 63, 602, 5761, 54096, 495964, 4447234; 1, 8, 84, 952, 10962, 125328, 1411228, 15629720, 170501039; 1, 9, 108, 1416, 19062, 257040, 3437028, 45421776, 593136513, 7661336692; 1, 10, 135, 2010, 30975, 481392, 7459230, 114696840, 1747674405, 26392662280, 395314147319; ... PROG (PARI) T(n, k)=local(F=1+x*O(x^n)); if(n

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 September 22 11:59 EDT 2023. Contains 365531 sequences. (Running on oeis4.)