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%I #11 Feb 13 2018 13:40:31
%S 1,1,5,51,791,16711,449575,14738537,570860449,25534320961,
%T 1296145448621,73644069770107,4631766294581959,319523289664700279,
%U 23992478864877747151,1948216141720780468561,170121586262631029818433,15897659114382366967974145,1583109774987253349677203349,167363833662976153803805436291,18721216520653602533835176495671
%N G.f.: Sum_{n>=0} binomial((n+1)^2, n)/(n+1) * x^n / (1 + x)^((n+1)^2).
%C Compare to: 1 = Sum_{n>=0} binomial(m*(n+1), n)/(n+1) * x^n / (1+x)^(m*(n+1)) holds for fixed m.
%e G.f.: A(x) = 1 + x + 5*x^2 + 51*x^3 + 791*x^4 + 16711*x^5 + 449575*x^6 + 14738537*x^7 + 570860449*x^8 + 25534320961*x^9 + 1296145448621*x^10 + ...
%e such that
%e A(x) = 1/(1+x) + C(4,1)/2*x/(1+x)^4 + C(9,2)/3*x^2/(1+x)^9 + C(16,3)/4*x^3/(1+x)^16 + C(25,4)/5*x^4/(1+x)^25 + C(36,5)/6*x^5/(1+x)^36 + C(49,6)/7*x^6/(1+x)^49 + ...
%e more explicitly,
%e A(x) = 1/(1+x) + 2*x/(1+x)^4 + 12*x^2/(1+x)^9 + 140*x^3/(1+x)^16 + 2530*x^4/(1+x)^25 + 62832*x^5/(1+x)^36 + 1997688*x^6/(1+x)^49 + ... + A091144(n+1)*x^n/(1+x)^((n+1)^2) + ...
%o (PARI) {a(n) = my(A = sum(m=0,n,binomial((m+1)^2,m)/(m+1)*x^m/(1+x +x*O(x^n))^((m+1)^2) ) ); polcoeff(A,n)}
%o for(n=0,25, print1(a(n),", "))
%Y Cf. A298695, A298696, A091144.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 09 2018
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