A320899 Expansion of e.g.f. exp(1/theta_4(x) - 1), where theta_4() is the Jacobi theta function.

1, 2, 12, 104, 1120, 14592, 221824, 3835904, 74262528, 1589016320, 37181031424, 943547716608, 25791165349888, 754934109863936, 23547020011929600, 779291847538638848, 27263652732032843776, 1005002283128197349376, 38921431600215853760512, 1579513585265275661189120

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: exp(-1 + Product_{k>=1} (1 + x^k)/(1 - x^k)).

a(0) = 1; a(n) = Sum_{k=1..n} A015128(k)*k!*binomial(n-1,k-1)*a(n-k).

Maple

seq(coeff(series(factorial(n)*(exp(-1+mul((1+x^k)/(1-x^k), k=1..n))), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 23 2018

Mathematica

nmax = 19; CoefficientList[Series[Exp[1/EllipticTheta[4, 0, x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Sum[PartitionsP[k - j] PartitionsQ[j], {j, 0, k}] k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A015128, A058892, A293840.

Sequence in context: A157328 A061632 A301833 * A194951 A104533 A216794

Adjacent sequences: A320896 A320897 A320898 * A320900 A320901 A320902

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 23 2018

Status

approved