# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a184356 Showing 1-1 of 1 %I A184356 #8 Nov 24 2014 22:46:40 %S A184356 1,1,2,10,75,757,9955,161608,3149491,72294325,1919933126,58189667167, %T A184356 1991123304634,76201510956909,3235630545496281,151399102211450842, %U A184356 7760065212106661217,433404831023513573519,26253103133315432898270,1717576707472491422233436,120912301935843736344714288 %N A184356 G.f.: Sum_{n>=0} x^n/[Sum_{k=0..n} C(n,k)^2*(-x)^k]^n. %H A184356 Paul D. Hanna, Table of n, a(n) for n = 0..100 %F A184356 G.f.: Sum_{n>=0} x^n * (1+x)^(-2*n^2 - n) / [Sum_{k>=0} C(n+k,k)^2*(-x)^k]^n. %e A184356 G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 75*x^4 + 757*x^5 + 9955*x^6 +... %e A184356 equals the sum of the series: %e A184356 A(x) = 1 + x/(1-x) + x^2/(1 - 2^2*x + x^2)^2 + %e A184356 + x^3/(1 - 3^2*x + 3^2*x^2 - x^3)^3 %e A184356 + x^4/(1 - 4^2*x + 6^2*x^2 - 4^2*x^3 + x^4)^4 %e A184356 + x^5/(1 - 5^2*x + 10^2*x^2 - 10^2*x^3 + 5^2*x^4 - x^5)^5 %e A184356 + x^6/(1 - 6^2*x + 15^2*x^2 - 20^2*x^3 + 15^2*x^4 - 6^2*x^5 + x^6)^6 +... %e A184356 The g.f. can also be expressed as: %e A184356 A(x) = 1 + x*(1+x)^-3/(1 - 2^2*x + 3^2*x^2 - 4^2*x^3 + 5^2*x^4 -+...) %e A184356 + x^2*(1+x)^-10/(1 - 3^2*x + 6^2*x^2 - 10^2*x^3 + 15^2*x^4 -+...)^2 %e A184356 + x^3*(1+x)^-21/(1 - 4^2*x + 10^2*x^2 - 20^2*x^3 + 35^2*x^4 -+...)^3 %e A184356 + x^4*(1+x)^-36/(1 - 5^2*x + 15^2*x^2 - 35^2*x^3 + 70^2*x^4 -+...)^4 %e A184356 + x^5*(1+x)^-55/(1 - 6^2*x + 21^2*x^2 - 56^2*x^3 + 126^2*x^4 -+...)^5 +... %o A184356 (PARI) {a(n)=polcoeff(sum(m=0, n, x^m/sum(k=0, m, binomial(m, k)^2*(-x)^k +x*O(x^n))^m), n)} %o A184356 for(n=0, 30, print1(a(n), ", ")) %o A184356 (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+x+x*O(x^n))^(-2*m^2-m)/sum(k=0, n-m+1, binomial(m+k, k)^2*(-x)^k+x*O(x^n))^m), n)} %o A184356 for(n=0, 30, print1(a(n), ", ")) %Y A184356 Cf. A184355, A183165, A183166. %K A184356 nonn %O A184356 0,3 %A A184356 _Paul D. Hanna_, Jan 12 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE