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A307955 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * ((1+x)^(5*n) - A(x))^(n+1), where A(0) = 0. 4
1, 9, 46, 344, 3586, 39676, 490036, 6669184, 97419116, 1519635734, 25170406452, 439941245653, 8081132624095, 155483518553143, 3124130586316551, 65389133324807724, 1422540686845941509, 32103883123046977644, 750278496443387818395, 18128963984900687497993, 452255024819251695443556, 11632687351726270908152086, 308130679955484625602559961, 8395760218678197725930082459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

FORMULA

G.f. A(x) satisfies:

(1) 1 = Sum_{n>=0} x^n * ((1+x)^(5*n) - A(x))^(n+1).

(2) 1 + x = Sum_{n>=0} x^n * (1+x)^(5*n*(n-1)) / (1 + x*(1+x)^(5*n)*A(x))^(n+1).

(3) 1 = Sum_{n>=0} x^n * (1-x)^(10*n+2) / ((1-x)^(5*n+1) - x*A(x/(1-x)))^(n+1).

(4) 1 = Sum_{n>=0} x^n * (1 - (1-x)^(5*n-5) * A(x/(1-x)))^n / (1-x)^(5*n^2-4*n-1)).

EXAMPLE

G.f.: A(x) = x + 9*x^2 + 46*x^3 + 344*x^4 + 3586*x^5 + 39676*x^6 + 490036*x^7 + 6669184*x^8 + 97419116*x^9 + 1519635734*x^10 + 25170406452*x^11 + ...

such that

1 = (1 - A(x)) + x*((1+x)^5 - A(x))^2 + x^2*((1+x)^10 - A(x))^3 + x^3*((1+x)^15 - A(x))^4 + x^4*((1+x)^20 - A(x))^5 + x^5*((1+x)^25 - A(x))^6 + x^6*((1+x)^30 - A(x))^7 + x^7*((1+x)^35 - A(x))^8 + ...

also

1 + x = 1/(1 + x*A(x)) + x/(1 + x*(1+x)^5*A(x))^2 + x^2*(1+x)^10/(1 + x*(1+x)^10*A(x))^3 + x^3*(1+x)^30/(1 + x*(1+x)^15*A(x))^4 + x^4*(1+x)^60/(1 + x*(1+x)^20*A(x))^5 + x^5*(1+x)^100/(1 + x*(1+x)^25*A(x))^6 + ...

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = polcoeff( sum(m=0, #A, x^m*((1+x +x*O(x^#A))^(5*m) - x*Ser(A))^(m+1) ), #A); ); A[n+1]}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A307940, A307952, A307953, A307954.

Sequence in context: A250722 A250776 A054140 * A110675 A265805 A274270

Adjacent sequences:  A307952 A307953 A307954 * A307956 A307957 A307958

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 07 2019

STATUS

approved

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Last modified September 18 21:53 EDT 2020. Contains 337173 sequences. (Running on oeis4.)