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A112502
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Third column of triangle A112500.
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2
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1, 10, 60, 282, 1149, 4272, 14932, 49996, 162369, 515886, 1613316, 4987542, 15290461, 46592452, 141350412, 427459320, 1289718225, 3884883570, 11688205420, 35135919730, 105558754461, 316995030840, 951656181540
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For a combinatorial formula see A112500, case k=3.
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FORMULA
| G.f.: 1/product((1-j*x)^(4-j), j=1..3) = 1/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).
a(n) = - 81/8 - (11/4)*(n+1) - (1/2)*binomial(n+2, 2) - 16*(n+1)*2^n + (243/8)*3^n, n>=0 (from partial fractions for g.f.).
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CROSSREFS
| Cf. A000295 (second column).
Sequence in context: A076160 A004406 A003472 * A083585 A155633 A002493
Adjacent sequences: A112499 A112500 A112501 * A112503 A112504 A112505
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 14 2005
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