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A301335 a(n) = [x^n] 1/(1 + (1/2)*n*(1 - theta_3(x))), where theta_3() is the Jacobi theta function. 2
1, 1, 4, 27, 260, 3175, 47304, 833147, 16941120, 390611331, 10070060200, 287028156162, 8962583345856, 304255011200647, 11156593415089808, 439452231820920000, 18505340390664634384, 829599437871129843839, 39447684087807950938908, 1983038000428208822539998, 105080571577382659860160800 (list; graph; refs; listen; history; text; internal format)
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: A240582 A328694 A302836 * A177379 A052813 A218653

Adjacent sequences:  A301332 A301333 A301334 * A301336 A301337 A301338

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 18 2018

STATUS

approved

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Last modified April 22 09:30 EDT 2021. Contains 343174 sequences. (Running on oeis4.)