Search: id:A077616
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%I A077616
%S A077616 1,10,63,324,1485,6318,25515,99144,373977,1377810,4979799,17714700,
%T A077616 62178597,215765046,741360195,2525407632,8537599665,28669116186,
%U A077616 95692860783,317684800980,1049522104701,3451916556990,11307641812443
%N A077616 Binomial transform of n^2*2^n/2.
%C A077616 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
%F A077616 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
%F A077616 G.f.: (1+x)/(1-3x)^3 - Paul Barry (pbarry(AT)wit.ie), Jun 09 2003
%F A077616 a(n)=n(2n+1)3^(n-2) - Paul Barry (pbarry(AT)wit.ie), Jul 24 2003
%Y A077616 Sequence in context: A027254 A159240 A055368 this_sequence A145885 A093953 
               A075755
%Y A077616 Adjacent sequences: A077613 A077614 A077615 this_sequence A077617 A077618 
               A077619
%K A077616 nonn
%O A077616 1,2
%A A077616 Karol A. Penson (penson(AT)lptl.jussieu.fr), Nov 12 2002

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