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A112532
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First differences of [0, A047970].
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5
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1, 1, 3, 9, 29, 101, 379, 1525, 6549, 29889, 144419, 736241, 3947725, 22201549, 130624587, 802180701, 5131183301, 34121977865, 235486915507, 1683925343929, 12458499203901, 95237603403381, 751291094637083, 6108883628141189, 51144808472958709, 440444879385258001
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..500
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FORMULA
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G.f.: (1-x)^2*( Sum_{n >= 0} x^n/(1 - (n+2)*x) ). - Peter Bala, Jul 09 2014
From Mathew Englander, Feb 28 2021: (Start)
a(n) = A089246(n+2,0) - A089246(n+1,0).
a(n) = n + Sum_{i = 0..n} (n-i-1)^2 * (n-i)^i. (End)
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MATHEMATICA
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a[n_]:= If[n==0, 1, n + Sum[(i-1)^2*i^(n-i), {i, 0, n}]];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jan 12 2022 *)
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PROG
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(PARI) a(n) = n + sum(i = 0, n, (n-i-1)^2 * (n-i)^i); \\ Michel Marcus, Mar 01 2021
(Sage) [n +sum((j-1)^2*j^(n-j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Jan 12 2022
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CROSSREFS
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Cf. A047970, A112531, A229046.
First differences of column 0 of triangle A089246 (beginning at row 1). With offset 1, first differences of column 0 of triangle A242431. Second differences of column 0 of triangle A101494.
Sequence in context: A278404 A148941 A079319 * A148942 A109432 A148943
Adjacent sequences: A112529 A112530 A112531 * A112533 A112534 A112535
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold, Sep 10 2005
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EXTENSIONS
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Corrected by D. S. McNeil, Aug 20 2010
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STATUS
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approved
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