A288343 - OEIS

A288343

Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*...*(1-x^8)).

1, 2, 4, 7, 12, 19, 30, 45, 67, 96, 136, 188, 258, 347, 463, 609, 795, 1025, 1313, 1665, 2099, 2624, 3262, 4026, 4945, 6035, 7332, 8859, 10660, 12764, 15226, 18083, 21402, 25230, 29647, 34713, 40525, 47155, 54719, 63307, 73056, 84074, 96524, 110536, 126301

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OFFSET

0,2

COMMENTS

Number of partitions of at most n into at most 8 parts.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Richard J. Mathar, Size of the Set of Residues of Integer Powers of Fixed Exponent, 2017.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,-1,1,-1,1,-1,1,1,1,-1,-1,1,-2,0,-1,1,0,2,-1,1,1,-1,-1,-1,1,-1,1,-1,1,0,1,0,-2,1).

FORMULA

a(n) = floor(1/1625702400*n^8 + 37/406425600*n^7 + 1951/348364800*n^6 + 3589/19353600*n^5 + 622523/174182400*n^4 + 73343/1814400*n^3 + 1085879/4233600*n^2 + 13073/16128*n + 52/49 - (n mod 2)*(2*n^3+111*n^2+1866*n)/73728 - (n mod 3)*n/486 + ((n^2+3*n+2) mod 4)*n/512). - Hoang Xuan Thanh, Aug 01 2026

MATHEMATICA

CoefficientList[Series[1/((1-x)Times@@(1-x^Range[8])), {x, 0, 50}], x] (* Harvey P. Dale, Dec 06 2017 *)

PROG

(PARI) my(x='x+O('x^99)); Vec(1/((1-x)*prod(i=1, 8, (1-x^i)))) \\ Altug Alkan, Mar 28 2018

CROSSREFS

Number of partitions of at most n into at most k parts: A002621 (k=4), A002622 (k=5), A288341 (k=6), A288342 (k=7), this sequence (k=8), A288344 (k=9), A288345 (k=10).

Cf. A288255.

Sequence in context: A288342 A347543 A343940 * A298414 A347544 A288344

Adjacent sequences: A288340 A288341 A288342 * A288344 A288345 A288346

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 08 2017

STATUS

approved