A341341 G.f. A(x) satisfies: 1 = Sum_{n>=0} (-1)^n * x^(n*(n+1)/2) * ((1+x)^n + A(x))^(n+1).

1, 4, 11, 29, 76, 207, 592, 1780, 5617, 18365, 61465, 209173, 720636, 2505401, 8773807, 30919540, 109581804, 390360666, 1397013258, 5020578459, 18111752521, 65564995435, 238097178090, 867136619465, 3166405246169, 11590402816879, 42520849230446

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Example

G.f.: A(x) = x + 4*x^2 + 11*x^3 + 29*x^4 + 76*x^5 + 207*x^6 + 592*x^7 + 1780*x^8 + 5617*x^9 + 18365*x^10 + 61465*x^11 + 209173*x^12 + ...
where
1 = (1 + A(x)) - x*((1+x) + A(x))^2 + x^3*((1+x)^2 + A(x))^3 - x^6*((1+x)^3 + A(x))^4 + x^10*((1+x)^4 + A(x))^5 - x^15*((1+x)^5 + A(x))^6 + ...
SPECIFIC VALUES.
At x = -1/2, 1 = Sum_{n>=0} (-1)^n * (-1/2)^(n*(n+1)/2) * (1/2^n + a)^(n+1), where a = 0.0849569238946083173319941875462909358145...
At x = 1/2, 1 = Sum_{n>=0} (-1)^n * (1/2)^(n*(n+1)/2) * ((3/2)^n + a)^(n+1), where a = 12.925265220825824331002181448511410832160...

Prog

(PARI) {a(n) = A=[1]; for(i=1, n, A = concat(A, 0);
A[#A] = -polcoeff( sum(m=0, sqrtint(2*#A)+1, (-1)^m * x^(m*(m+1)/2)*((1+x +x*O(x^#A))^m + x*Ser(A))^(m+1) ), #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A027972 A098149 A002878 * A124861 A369844 A351438

Adjacent sequences: A341338 A341339 A341340 * A341342 A341343 A341344

Keyword

nonn

Author

Paul D. Hanna, Feb 09 2021

Status

approved