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Search: id:A077616
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| A077616 |
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Binomial transform of n^2*2^n/2. |
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+0
4
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| 1, 10, 63, 324, 1485, 6318, 25515, 99144, 373977, 1377810, 4979799, 17714700, 62178597, 215765046, 741360195, 2525407632, 8537599665, 28669116186, 95692860783, 317684800980, 1049522104701, 3451916556990, 11307641812443
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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With a leading zero, this is second binomial transform of the hexagonal numbers A000384 (with leading zero). - Paul Barry (pbarry(AT)wit.ie), Jun 09 2003
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FORMULA
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E.g.f: exp(3*x)*(x+2*x^2) O.g.f: 1/3*x^(3/4)*3^(3/4)/(-(3*x+1)/(3*x-1)+1)^(1/4)*(-(3*x+1)/(3*x-1)-1)^(1/4)*hypergeom([ -1, 2], [3/2], 3*x/(3*x-1))/(3*x-1)^2, which can also be represented as associated Legendre function: 1/6*x^(3/4)*Pi^(1/2)*3^(3/4)*LegendreP(1, -1/2, (3*x+1)/(1-3*x))/(3*x-1)^2
G.f.: (1+x)/(1-3x)^3 - Paul Barry (pbarry(AT)wit.ie), Jun 09 2003
a(n)=n(2n+1)3^(n-2) - Paul Barry (pbarry(AT)wit.ie), Jul 24 2003
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CROSSREFS
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Sequence in context: A027254 A159240 A055368 this_sequence A145885 A093953 A075755
Adjacent sequences: A077613 A077614 A077615 this_sequence A077617 A077618 A077619
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KEYWORD
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nonn
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AUTHOR
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Karol A. Penson (penson(AT)lptl.jussieu.fr), Nov 12 2002
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