A274322 Number of partitions of n^2 into at most five parts.

1, 1, 5, 23, 101, 377, 1226, 3507, 9027, 21224, 46262, 94512, 182702, 336666, 595085, 1014091, 1673243, 2682685, 4192118, 6401314, 9572962, 14047457, 20260601, 28763703, 40247228, 55567352, 75776769, 102158957, 136267461, 179969238, 235493851, 305487369

Offset: 0

Author

Colin Barker, Jun 20 2016

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

A subsequence of A001401.

Programs

PARI

\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
b(n) = round(((n+5)^4+10*((n+5)^3+(n+5)^2)-75*(n+5)-45*(n+5)*(-1)^(n+5))/2880)
vector(40, n, n--; b(n^2))

Formula

Coefficient of x^(n^2) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).

a(n) = A001401(n^2).

Empirical g.f.: (1 -3*x +4*x^2 +13*x^3 +21*x^4 +63*x^5 +138*x^6 +204*x^7 +257*x^8 +280*x^9 +267*x^10 +201*x^11 +128*x^12 +67*x^13 +31*x^14 +6*x^15 +x^16 +x^17) / ((1 -x)^9*(1 +x)^3*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4)).