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A290792 Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)^2*(k+2)/12)). 3
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 18, 18, 19, 19, 20, 20, 22, 22, 23, 23, 25, 25, 27, 27, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 45, 45, 47, 47, 49, 49, 52, 52, 54, 54, 57 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Number of partitions of n into nonzero 4-dimensional pyramidal numbers (A002415).

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)^2*(k+2)/12)).

EXAMPLE

a(12) = 3 because we have [6, 6], [6, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

MAPLE

N:= 100: # for a(0)..a(N)

P:= 1:

for k from 1 do

  e:= k*(k+1)^2*(k+2)/12;

  if e > N then break fi;

  P:= P/(1-x^e);

od:

S:= series(P, x, N+1):

[seq](coeff(S, x, n), n=0..N); # Robert Israel, Aug 28 2019

MATHEMATICA

nmax = 90; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)^2 (k + 2)/12)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000330, A001156, A002415, A279220, A290573.

Sequence in context: A262694 A137588 A033271 * A279757 A251550 A279221

Adjacent sequences:  A290789 A290790 A290791 * A290793 A290794 A290795

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 15 2017

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)