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A227934 G.f.: Sum_{n>=0} x^n / (1-x)^(n^4). 3

%I

%S 1,1,2,18,219,4395,129280,4970984,257765641,16781325293,1348125117404,

%T 132465548869248,15490711962965785,2134540479514352751,

%U 343307151209151099650,63606662918084631874716,13470938654397531939066909,3238387688528230753569245297,876825599524773154743990986391

%N G.f.: Sum_{n>=0} x^n / (1-x)^(n^4).

%F a(n) = Sum_{k=0..n} binomial(k^4 + n-k-1, n-k).

%e G.f.: A(x) = 1 + x + 2*x^2 + 18*x^3 + 219*x^4 + 4395*x^5 + 129280*x^6 +...

%e where

%e A(x) = 1 + x/(1-x) + x^2/(1-x)^16 + x^3/(1-x)^81 + x^4/(1-x)^256 + x^5/(1-x)^625 + x^6/(1-x)^1296 + x^7/(1-x)^2401 +...

%o (PARI) {a(n)=polcoeff(sum(k=0,n,x^k/(1-x+x*O(x^n))^(k^4)),n)}

%o for(n=0,20,print1(a(n),", "))

%o (PARI) {a(n)=sum(k=0,n,binomial(k^4+n-k-1, n-k))}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A178325, A230050, A227935.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 06 2013

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Last modified October 25 10:46 EDT 2021. Contains 348239 sequences. (Running on oeis4.)