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A274322 Number of partitions of n^2 into at most five parts. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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)).
PROG
(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))
CROSSREFS
A subsequence of A001401.
Sequence in context: A073682 A034958 A229008 * A085350 A113443 A124999
KEYWORD
nonn
AUTHOR
Colin Barker, Jun 20 2016
STATUS
approved

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Last modified May 25 04:23 EDT 2024. Contains 372782 sequences. (Running on oeis4.)