A301335 a(n) = [x^n] 1/(1 + (1/2)*n*(1 - theta_3(x))), where theta_3() is the Jacobi theta function.

1, 1, 4, 27, 260, 3175, 47304, 833147, 16941120, 390611331, 10070060200, 287028156162, 8962583345856, 304255011200647, 11156593415089808, 439452231820920000, 18505340390664634384, 829599437871129843839, 39447684087807950938908, 1983038000428208822539998, 105080571577382659860160800

Offset

0,3

Comments

Number of compositions (ordered partitions) of n into squares of n kinds.

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Formula

a(n) = [x^n] 1/(1 - n*Sum_{k>=1} x^(k^2)).

a(n) ~ n^n * (1 + 1/n^2 - 3/n^3 + 1/(2*n^4) - 13/(2*n^5) + 127/(6*n^6) - 4/n^7 + 335/(8*n^8) - 665/(4*n^9) + 337/(15*n^10) + ...). - Vaclav Kotesovec, Mar 19 2018

Mathematica

Table[SeriesCoefficient[1/(1 + (1/2) n (1 - EllipticTheta[3, 0, x])), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - n Sum[x^k^2, {k, 1, n}]), {x, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A000290, A006456, A240944, A300974, A301334.

Sequence in context: A360835 A374812 A302836 * A362701 A376107 A177379

Adjacent sequences: A301332 A301333 A301334 * A301336 A301337 A301338

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 18 2018

Status

approved