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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338306 O.g.f. A(x) satisfies: A(x) = 1/(1 - x * (d/dx x + x^2*A(x)) ). 1
 1, 1, 3, 8, 29, 106, 438, 1869, 8499, 39926, 195332, 983262, 5099640, 27104535, 147565543, 820663322, 4658281691, 26943982072, 158681719362, 950517101448, 5787148086216, 35785974189746, 224625453101666, 1430389538402366, 9236235576715260, 60448170602414931, 400818049588802391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..500 FORMULA O.g.f. A(x) satisfies: (1) A(x) = 1/(1 - x * (d/dx x + x^2*A(x)) ). (2) 0 = [x^n] exp( n * (x + x^2*A(x)) ) / A(x), for n > 0. EXAMPLE O.g.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 29*x^4 + 106*x^5 + 438*x^6 + 1869*x^7 + 8499*x^8 + 39926*x^9 + 195332*x^10 + 983262*x^11 + 5099640*x^12 + ... where 1/A(x) = 1 - x - 2*x^2 - 3*x^3 - 12*x^4 - 40*x^5 - 174*x^6 - 742*x^7 - 3504*x^8 - 16821*x^9 - 84990*x^10 - ... and d/dx x + x^2*A(x) = 1 + 2*x + 3*x^2 + 12*x^3 + 40*x^4 + 174*x^5 + 742*x^6 + 3504*x^7 + 16821*x^8 +  + 84990*x^9 + ... PROG (PARI) /* A(x) = 1/(1 - x*( d/dx x + x^2*A(x) )) */ {a(n) = my(A=1+x); for(i=1, n, A=1/(1 - x*deriv(x + x^2*A+x*O(x^n)))); polcoeff(A, n)} for(n=0, 20, print1(a(n), ", ")) (PARI) /* [x^n] exp( n * (x + x^2*A(x)') ) / A(x) = 0 */ {a(n) = my(A=[1], m); for(i=1, n, A=concat(A, 0); m=#A; A[m] = Vec( exp( (m-1)*(x+x^2*Ser(A)) ) / Ser(A) )[m] ); A[n+1]} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A338301, A183607. Sequence in context: A148874 A022017 A148875 * A148876 A245889 A013309 Adjacent sequences:  A338303 A338304 A338305 * A338307 A338308 A338309 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 21 2020 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 September 18 10:51 EDT 2021. Contains 347518 sequences. (Running on oeis4.)