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A092365
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Coefficient of X^2 in expansion of (1+n*X+n*X^2)^n.
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1
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1, 8, 36, 112, 275, 576, 1078, 1856, 2997, 4600, 6776, 9648, 13351, 18032, 23850, 30976, 39593, 49896, 62092, 76400, 93051, 112288, 134366, 159552, 188125, 220376, 256608, 297136, 342287, 392400, 447826, 508928, 576081, 649672, 730100, 817776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=n^2*(binomial(n, 2)+1)
G.f.: x*(1+3*x+6*x^2+2*x^3)/(1-x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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MAPLE
| a:=n->add(n+add(binomial(n, 2), j=1..n), j=1..n):seq(a(n), n=1..35); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
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MATHEMATICA
| Coefficient[Table[Expand[(1+n x+n x^2)^n], {n, 60}], x, 2] (* From Harvey P. Dale, Mar 13 2011 *)
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PROG
| (PARI) q(n)=(1+n*X+n*X^2)^n; for(i=1, 40, print1(", "polcoeff(q(i), 2)))
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CROSSREFS
| Sequence in context: A035006 A032768 A006636 * A014343 A162596 A051192
Adjacent sequences: A092362 A092363 A092364 * A092366 A092367 A092368
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Mar 19 2004
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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