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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

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Last modified September 18 10:51 EDT 2021. Contains 347518 sequences. (Running on oeis4.)