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

0,5

Comments

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

Links

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

Example

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).

Prog

(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)}

Crossrefs

Cf. A162552, A010052, A162416 (variant).

Sequence in context: A029716 A284521 A360029 * A310072 A310073 A310074

Adjacent sequences: A162550 A162551 A162552 * A162554 A162555 A162556

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2009

Status

approved