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A046770
Number of partitions of n with equal number of parts congruent to each of 0, 1, 2 and 3 (mod 4).
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 10, 0, 1, 0, 20, 0, 4, 0, 35, 0, 14, 0, 57, 0, 36, 0, 88, 0, 85, 0, 134, 0, 177, 0, 205, 0, 348, 0, 321, 0, 638, 0, 519, 0, 1126, 0, 866, 0, 1905, 0, 1473, 0, 3141, 0, 2530, 0, 5046, 0, 4341, 0, 7976, 0, 7387, 0, 12416, 0, 12415
OFFSET
0,15
LINKS
FORMULA
G.f.: Sum_{k>=0} x^(10*k)/(Product_{j=1..k} 1 - x^(4*j))^4. - Andrew Howroyd, Sep 16 2019
MATHEMATICA
kmax = 75; Sum[x^(10k)/Product[1 - x^(4j), {j, 1, k}]^4, {k, 0, kmax}] + O[x]^kmax // CoefficientList[#, x]& (* Jean-François Alcover, Sep 23 2019 *)
PROG
(PARI) seq(n)={Vec(sum(k=0, n\10, x^(10*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^4) + O(x*x^n))} \\ Andrew Howroyd, Sep 16 2019
CROSSREFS
Cf. A046765.
Sequence in context: A327054 A101419 A060278 * A046782 A074037 A285132
KEYWORD
nonn
STATUS
approved