cp's OEIS Frontend

A215242 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1+x)^((n+2)^2).

%I A215242 #7 Dec 12 2024 02:54:06
%S A215242 1,4,26,256,3489,61696,1352518,35566368,1094499820,38670814348,
%T A215242 1545160614694,68970980789472,3404652821768232,184295822142051600,
%U A215242 10861040169788302030,692560292664515634112,47527552597795293035916,3493783983256399634130360,273974326317024551368217200
%N A215242 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1+x)^((n+2)^2).
%C A215242 Column 2 of triangle A215241.
%e A215242 G.f.: 1 = 1/(1+x)^4 + 4*x/(1+x)^9 + 26*x^2/(1+x)^16 + 256*x^3/(1+x)^25 + 3489*x^4/(1+x)^36 + 61696*x^5/(1+x)^49 +...
%e A215242 Also forms the final terms in rows of the triangle where row n+1 equals the partial sums of row n with the final term repeated 2*n+1 times, starting with '[1,1,1,1]' in row 1, as illustrated by:
%e A215242 1, 1,  1,  1;
%e A215242 1, 2,  3,  4,  4,   4,   4,   4;
%e A215242 1, 3,  6, 10, 14,  18,  22,  26,  26,  26,  26,  26,  26,   26;
%e A215242 1, 4, 10, 20, 34,  52,  74, 100, 126, 152, 178, 204, 230,  256,  256,  256,  256,  256,  256,  256,  256,  256;
%e A215242 1, 5, 15, 35, 69, 121, 195, 295, 421, 573, 751, 955, 1185, 1441, 1697, 1953, 2209, 2465, 2721, 2977, 3233, 3489, 3489, 3489, 3489, 3489, 3489, 3489, 3489, 3489; ...
%o A215242 (PARI) {a(n)=if(n==0,1,polcoeff(1-sum(k=0, n-1, a(k)*x^k/(1+x+x*O(x^n))^((k+2)^2)), n))}
%o A215242 for(n=0,21,print1(a(n)", "))
%Y A215242 Cf. A215241, A177447, A215243, A133316.
%K A215242 nonn
%O A215242 0,2
%A A215242 _Paul D. Hanna_, Aug 06 2012