A308027 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (1 + n*x - A(x))^(n+1), where A(0) = 0.

1, 1, 2, 5, 16, 55, 211, 858, 3709, 16799, 79393, 389476, 1975794, 10336925, 55626033, 307348959, 1740424149, 10087499430, 59764588797, 361575122501, 2231594755060, 14039189350213, 89957652033096, 586694050333245, 3892099566201798, 26248657606212596, 179864639698235287, 1251657405383723002, 8841433832652547890, 63367819640545183277, 460621983117854333354, 3394551331802426437715

Offset

1,3

Links

Table of n, a(n) for n=1..32.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 16*x^5 + 55*x^6 + 211*x^7 + 858*x^8 + 3709*x^9 + 16799*x^10 + 79393*x^11 + 389476*x^12 + 1975794*x^13  + ...
such that
1 = (1 - A(x)) + x*(1 + x - A(x))^2 + x^2*(1 + 2*x - A(x))^3 + x^3*(1 + 3*x - A(x))^4 + x^4*(1 + 4*x - A(x))^5 + x^5*(1 + 5*x - A(x))^6 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(n=0, #A, x^n * ( (1 + n*x) - x*Ser(A) )^(n+1) ), #A) ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A176828 A149972 A026106 * A066642 A333233 A019988

Adjacent sequences: A308024 A308025 A308026 * A308028 A308029 A308030

Keyword

nonn

Author

Paul D. Hanna, May 14 2019

Status

approved