A162553 G.f.: A(x) = exp( Sum_{n>=1} A162552(n)^2*x^n/n ) where the l.g.f. of A162552 is the log of the characteristic function of the squares.

1, 1, 1, 1, 3, 6, 10, 15, 18, 35, 73, 143, 230, 296, 416, 753, 1673, 2934, 4203, 5654, 9135, 17881, 33102, 52787, 73749, 107869, 189629, 359107, 619296, 923833, 1306855, 2065717, 3776424, 6823452, 10935160, 15822727, 23395694, 39675378

Offset: 0

Author

Paul D. Hanna, Jul 06 2009

Keywords

• nonn

Comments

A162552 is defined by: exp( Sum_{n>=1} A162552(n)*x^n/n ) = Sum_{n>=0} x^(n^2).

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 15*x^6 +...
log(A(x)) = x + x^2/2 + x^3/3 + 9*x^4/4 + 16*x^5/5 + 25*x^6/6 + 36*x^7/7 +...+ A162552(n)^2*x^n/n +...
Let L(x) = x - 1*x^2/2 + 1*x^3/3 + 3*x^4/4 - 4*x^5/5 + 5*x^6/6 - 6*x^7/7 +...+ A162552(n)*x^n/n +... then
exp(L(x)) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 +...+ x^(n^2) +...
is the characteristic function of the squares (A010052).
		

Links

• Paul D. Hanna, Table of n, a(n), n = 0..330.

Crossrefs

Cf. A162552, A010052, A162416 (variant).

Programs

PARI

{a(n)=local(Q=sum(m=0,n,x^(m^2))+x*O(x^n),A); A=exp(sum(k=1,n,polcoeff(log(Q),k)^2*k*x^k)+x*O(x^n));polcoeff(A,n)}