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

1, 1, 2, 18, 219, 4395, 129280, 4970984, 257765641, 16781325293, 1348125117404, 132465548869248, 15490711962965785, 2134540479514352751, 343307151209151099650, 63606662918084631874716, 13470938654397531939066909, 3238387688528230753569245297, 876825599524773154743990986391

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Example

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

Prog

(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-x+x*O(x^n))^(k^4)), n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=sum(k=0, n, binomial(k^4+n-k-1, n-k))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A178325, A230050, A227935.

Sequence in context: A279045 A155666 A355723 * A349652 A364825 A245112

Adjacent sequences: A227931 A227932 A227933 * A227935 A227936 A227937

Keyword

nonn

Author

Paul D. Hanna, Oct 06 2013

Status

approved