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A327683 Expansion of Product_{k>0} (1+sqrt(1+4*x^k))/2. 3
1, 1, 0, 4, -5, 17, -40, 144, -459, 1517, -5111, 17747, -62074, 219292, -782602, 2816664, -10205754, 37203230, -136360106, 502219652, -1857659296, 6897983144, -25704335380, 96090440940, -360265425619, 1354343161419, -5103948546609, 19278502980063, -72972099256954 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..28.

MAPLE

N:= 40:

P:= mul((1+sqrt(1+4*x^k))/2, k=1..N):

S:= series(P, x, N+1):

seq(coeff(S, x, j), j=0..N); # Robert Israel, Sep 22 2019

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1+Sqrt[1+4*x^k])/2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 22 2019 *)

PROG

(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+sqrt(1+4*x^k))/2))

(PARI) N=66; x='x+O('x^N); Vec(prod(i=1, N, 1-sum(j=1, N\i, (-1)^j*binomial(2*j-2, j-1)*x^(i*j)/j)))

CROSSREFS

Convolution inverse of A327682.

Cf. A000009, A268498, A327684.

Sequence in context: A306161 A119997 A010361 * A060289 A215024 A066879

Adjacent sequences:  A327680 A327681 A327682 * A327684 A327685 A327686

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 22 2019

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)