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A280352 Expansion of Sum_{k>=1} (x/(1 - x))^(k*(k+1)/2). 1
1, 1, 2, 4, 7, 12, 22, 43, 85, 164, 308, 573, 1079, 2081, 4097, 8129, 16049, 31315, 60402, 115806, 222416, 430791, 843987, 1670054, 3322167, 6606936, 13078586, 25714238, 50230292, 97708338, 189921842, 370216757, 725680489, 1431888173, 2842060970, 5662371069 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of compositions of n into a triangular number of parts.

LINKS

Table of n, a(n) for n=1..36.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=1} (x/(1 - x))^(k*(k+1)/2).

EXAMPLE

a(5) = 7 because we have:

[1]  [5]

[2]  [3, 1, 1]

[3]  [1, 3, 1]

[4]  [1, 1, 3]

[5]  [2, 2, 1]

[6]  [2, 1, 2]

[7]  [1, 2, 2]

MATHEMATICA

nmax = 36; Rest[CoefficientList[Series[Sum[(x/(1 - x))^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]]

nmax = 40; Rest[CoefficientList[Series[-1 + EllipticTheta[2, 0, Sqrt[x/(1-x)]]/(2*(x/(1-x))^(1/8)), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jan 01 2017 *)

CROSSREFS

Cf. A000217, A052467, A103198, A280351.

Sequence in context: A127542 A023432 A072641 * A135360 A082548 A270995

Adjacent sequences:  A280349 A280350 A280351 * A280353 A280354 A280355

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Jan 01 2017

STATUS

approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)