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

1, 4, 26, 256, 3489, 61696, 1352518, 35566368, 1094499820, 38670814348, 1545160614694, 68970980789472, 3404652821768232, 184295822142051600, 10861040169788302030, 692560292664515634112, 47527552597795293035916, 3493783983256399634130360, 273974326317024551368217200

Offset: 0

Author

Paul D. Hanna, Aug 06 2012

Keywords

• nonn

Comments

Column 2 of triangle A215241.

Examples

			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 +...
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:
1, 1,  1,  1;
1, 2,  3,  4,  4,   4,   4,   4;
1, 3,  6, 10, 14,  18,  22,  26,  26,  26,  26,  26,  26,   26;
1, 4, 10, 20, 34,  52,  74, 100, 126, 152, 178, 204, 230,  256,  256,  256,  256,  256,  256,  256,  256,  256;
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; ...
		

Crossrefs

Cf. A215241, A177447, A215243, A133316.

Programs

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))}
for(n=0,21,print1(a(n)", "))