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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A282064 A029716 A284521 * A310072 A310073 A310074

Adjacent sequences:  A162550 A162551 A162552 * A162554 A162555 A162556

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 06 2009

STATUS

approved

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Last modified October 15 13:52 EDT 2018. Contains 316236 sequences. (Running on oeis4.)