A299434 G.f. A(x) satisfies: 1 = Sum_{n>=0} binomial((n+1)^2,n)/(n+1)^2 * x^n / A(x)^((n+1)^2).

1, 1, 1, 6, 77, 1451, 35730, 1082481, 38913817, 1619979291, 76724619427, 4077896446598, 240566693095072, 15609120639706252, 1105414601508493001, 84881459931003622118, 7026832554316541379141, 624014794413319426058889, 59184228450018585954486975, 5971678912361406721742217080, 638782082648832471805820934833, 72213308562202419209594988387550, 8603323896642095980014195130664418

Offset

0,4

Comments

Compare to: 1 = Sum_{n>=0} binomial(m*(n+1), n)/(n+1) * x^n / (1+x)^(m*(n+1)) holds for fixed m.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Example

G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 77*x^4 + 1451*x^5 + 35730*x^6 + 1082481*x^7 + 38913817*x^8 + 1619979291*x^9 + 76724619427*x^10 +...
such that
1 = 1/A(x) + C(4,1)/4*x/A(x)^4 + C(9,2)/9*x^2/A(x)^9 + C(16,3)/16*x^3/A(x)^16 + C(25,4)/25*x^4/A(x)^25 + C(36,5)/36*x^5/A(x)^36 + C(49,6)/49*x^6/A(x)^49 + ...
more explicitly,
1 = 1/A(x) + x/A(x)^4 + 4*x^2/A(x)^9 + 35*x^3/A(x)^16 + 506*x^4/A(x)^25 + 10472*x^5/A(x)^36 + 285384*x^6/A(x)^49 + ... + A143669(n)*x^n/A(x)^((n+1)^2) + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = Vec(sum(n=0, #A, binomial((n+1)^2, n)/(n+1)^2 * x^n/Ser(A)^((n+1)^2-1) ))); G=Ser(A); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A298692, A143669.

Sequence in context: A282783 A215551 A154645 * A355764 A301834 A366540

Adjacent sequences: A299431 A299432 A299433 * A299435 A299436 A299437

Keyword

nonn

Author

Paul D. Hanna, Feb 13 2018

Status

approved