A322853 Number of compositions (ordered partitions) of n into pentagonal pyramidal numbers (A002411).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 44, 57, 74, 96, 124, 159, 205, 265, 343, 444, 574, 740, 954, 1231, 1590, 2055, 2656, 3430, 4428, 5716, 7380, 9531, 12312, 15902, 20536, 26518, 34242, 44218, 57106, 73751, 95245, 122999, 158837, 205117

Offset

0,7

Links

Table of n, a(n) for n=0..51.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Index entries for sequences related to compositions

Formula

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

Mathematica

nmax = 51; CoefficientList[Series[1/(1 - Sum[x^(k^2 (k + 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A002411, A181324, A279221, A282582, A322340, A322801, A322854, A322855, A322856.

Sequence in context: A017900 A005708 A367637 * A322801 A322798 A085793

Adjacent sequences: A322850 A322851 A322852 * A322854 A322855 A322856

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2018

Status

approved