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A222057
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Triangle read by rows: coefficients of harmonic-geometric polynomials.
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8
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1, 1, 3, 1, 9, 11, 1, 21, 66, 50, 1, 45, 275, 500, 274, 1, 93, 990, 3250, 4110, 1764, 1, 189, 3311, 17500, 38360, 37044, 13068, 1, 381, 10626, 85050, 287700, 469224, 365904, 109584, 1, 765, 33275, 388500, 1904574, 4667544, 6037416, 3945024, 1026576, 1, 1533, 102630, 1705250, 11651850, 40266828, 76839840, 82188000, 46195920, 10628640
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OFFSET
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1,3
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LINKS
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FORMULA
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The n-th polynomial is Sum_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|*x^k.
(The k=0 term is always 0. Sequence lists coefficients of x, x^2, x^3, ... - M. F. Hasler, Jul 12 2018)
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EXAMPLE
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Triangle begins:
1;
1, 3;
1, 9, 11;
1, 21, 66, 50;
1, 45, 275, 500, 274;
1, 93, 990, 3250, 4110, 1764;
1, 189, 3311, 17500, 38360, 37044, 13068;
1, 381, 10626, 85050, 287700, 469224, 365904, 109584;
...
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PROG
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(PARI) A222057(n, k)=stirling(n, k, 2)*abs(stirling(k+1, 2)) \\ with 1 <= k <= n: vector(8, n, vector(n, k, A222057(n, k))). - M. F. Hasler, Jul 12 2018
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CROSSREFS
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Row sums give A222058. See A222060 for another version (including row & column 0).
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KEYWORD
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AUTHOR
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STATUS
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approved
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