A320898 Expansion of e.g.f. exp(theta_3(x) - 1), where theta_3() is the Jacobi theta function.

1, 2, 4, 8, 64, 512, 2944, 13568, 134656, 2371328, 29676544, 268141568, 2560761856, 53154824192, 991944441856, 13085180592128, 187309143556096, 4400237083492352, 105779411022905344, 1939709049732595712, 37680665654471950336, 882429584512554893312, 23052947736212625424384

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: exp(2*Sum_{k>=1} x^(k^2)).

a(0) = 1; a(n) = Sum_{k=1..n} A000122(k)*k!*binomial(n-1,k-1)*a(n-k).

Maple

seq(coeff(series(factorial(n)*(exp(2*add(x^(k^2), k=1..n))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 23 2018

Mathematica

nmax = 22; CoefficientList[Series[Exp[EllipticTheta[3, 0, x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[SquaresR[1, k] k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A000122, A205800.

Sequence in context: A362343 A065549 A067507 * A068994 A167182 A058345

Adjacent sequences: A320895 A320896 A320897 * A320899 A320900 A320901

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 23 2018

Status

approved