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A337799 Number of compositions (ordered partitions) of the n-th n-gonal pyramidal number into n-gonal pyramidal numbers. 4
1, 1, 2, 15, 2780, 94947913, 5470124262136760, 5979009355803053742719666641, 1610158754567753309521653012201612266212334009, 1566217729562552701894041200097975651072376485590145959656670312797530 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Pyramidal Number
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
Sequence in context: A096232 A193869 A320768 * A064171 A365628 A135085
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 22 2020
STATUS
approved

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Last modified July 12 05:51 EDT 2024. Contains 374237 sequences. (Running on oeis4.)