A276279 Number of triangular partitions of n of order 8.

1, 8, 36, 127, 386, 1050, 2632, 6187, 13789, 29396, 60336, 119818, 231140, 434555, 798320, 1436294, 2535511, 4398876, 7510668, 12635844, 20969143, 34357138, 55625853, 89060282, 141101197, 221350031, 344008194, 529925620, 809497788, 1226738457

Offset

0,2

Links

Table of n, a(n) for n=0..29.

L. Carlitz, R. Scoville, A generating function for triangular partitions, Math. Comp. 29 (1975) 67-77.

Formula

G.f.: 1/((1-x)^8*(1-x^3)^7*(1-x^5)^6*(1-x^7)^5*(1-x^9)^4*(1-x^11)^3*(1-x^13)^2*(1-x^15)).

Mathematica

CoefficientList[Series[1/((1-x)^8 (1-x^3)^7 (1-x^5)^6 (1-x^7)^5 (1-x^9)^4 (1-x^11)^3 (1-x^13)^2 (1-x^15)), {x, 0, 50}], x]

Prog

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^8*(1-x^3)^7*(1-x^5)^6*(1-x^7)^5*(1-x^9)^4*(1-x^11)^3*(1-x^13)^2*(1-x^15)))); // Corrected by Georg Fischer, May 19 2019

Crossrefs

Cf. similar sequences listed in A276235.

Sequence in context: A347751 A341222 A213581 * A210379 A131123 A055910

Adjacent sequences: A276276 A276277 A276278 * A276280 A276281 A276282

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 01 2016

Extensions

Terms a(10) onward corrected by Georg Fischer, May 19 2019

Status

approved