A337799 Number of compositions (ordered partitions) of the n-th n-gonal pyramidal number into n-gonal pyramidal numbers.

1, 1, 2, 15, 2780, 94947913, 5470124262136760, 5979009355803053742719666641, 1610158754567753309521653012201612266212334009, 1566217729562552701894041200097975651072376485590145959656670312797530

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index entries for sequences related to compositions

Index to sequences related to pyramidal numbers

Formula

a(n) = [x^p(n,n)] 1 / (1 - Sum_{k=1..n} x^p(n,k)), where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.

Example

a(3) = 15 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 4, 1], [4, 1, 1, 4], [1, 4, 4, 1], [1, 4, 1, 4], [1, 1, 4, 4], [4, 1, 1, 1, 1, 1, 1], [1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 1], [1, 1, 1, 4, 1, 1, 1], [1, 1, 1, 1, 4, 1, 1], [1, 1, 1, 1, 1, 4, 1], [1, 1, 1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Crossrefs

Cf. A006484, A224677, A337764, A337797, A337798.

Sequence in context: A096232 A193869 A320768 * A064171 A365628 A135085

Adjacent sequences: A337796 A337797 A337798 * A337800 A337801 A337802

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 22 2020

Status

approved