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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 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

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