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A274253 Number of partitions of n^7 into at most three parts. 5
1, 1, 1430, 399675, 22377814, 508665365, 6530486977, 56519001176, 366504924502, 1906401762732, 8333338333334, 31645829208856, 106993223294977, 328114730182533, 926000621503254, 2432743920878907, 6004799637378390, 14031485751786081, 31234447604616769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

Coefficient of x^(n^7) in 1/((1-x)*(1-x^2)*(1-x^3)).

G.f.: (1 -12*x +1494*x^2 +380888*x^3 +17292525*x^4 +248136510*x^5 +1532347656*x^6 +4916629962*x^7 +9347647209*x^8 +11464268960*x^9 +9347652702*x^10 +4916635404*x^11 +1532337619*x^12 +248138478*x^13 +17294340*x^14 +380562*x^15 +1302*x^16) / ((1 -x)^15*(1 +x)*(1 +x +x^2)).

a(n) = A001399(n^7) = round((n^7+3)^2/12). - Alois P. Heinz, Jun 16 2016

MATHEMATICA

CoefficientList[Series[(1-12x+1494x^2+380888x^3+17292525x^4+248136510x^5+1532347656x^6+ 4916629962x^7+ 9347647209x^8+11464268960x^9+9347652702x^10+ 4916635404x^11+ 1532337619x^12+ 248138478x^13+17294340x^14+380562x^15+1302x^16)/((1-x)^15(1+x)(1+x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, -77, 274, -650, 1078, -1274, 1066, -572, 0, 572, -1066, 1274, -1078, 650, -274, 77, -13, 1}, {1, 1, 1430, 399675, 22377814, 508665365, 6530486977, 56519001176, 366504924502, 1906401762732, 8333338333334, 31645829208856, 106993223294977, 328114730182533, 926000621503254, 2432743920878907, 6004799637378390, 14031485751786081}, 30] (* Harvey P. Dale, Dec 09 2022 *)

PROG

(PARI)

\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).

b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))

vector(50, n, n--; b(n^7))

CROSSREFS

A subsequence of A001399.

Cf. A274250 (n^2), A274251 (n^3), A274252 (n^5), A274254 (n^11).

Sequence in context: A258495 A258396 A215548 * A227598 A321977 A147695

Adjacent sequences: A274250 A274251 A274252 * A274254 A274255 A274256

KEYWORD

nonn

AUTHOR

Colin Barker, Jun 16 2016

STATUS

approved

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Last modified March 25 05:54 EDT 2023. Contains 361511 sequences. (Running on oeis4.)