A247030 - OEIS

A247030

G.f.: 1 = Sum_{n>=0} a(n)*x^n * [ Sum_{k=0..n+1} binomial(n+1, k)^2*(-x)^k ]^3.

1, 3, 33, 739, 26826, 1404627, 98887630, 8932402203, 1001208571836, 135804313969750, 21859401699427485, 4110314757616106643, 891280031429868425060, 220472752705231812870426, 61644750354633249317246358, 19327988780537395352731009379, 6748646674845561326467643182776

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OFFSET

0,2

COMMENTS

Compare to a g.f. of A006632(n) = 3*binomial(4*n+3,n)/(4*n+3):

1 = Sum_{n>=0} A006632(n)*x^n * [ Sum_{k=0..n+1} binomial(n+1, k)*(-x)^k ]^3.

LINKS

Table of n, a(n) for n=0..16.

EXAMPLE

G.f.: A(x) = 1 + 3*x + 33*x^2 + 739*x^3 + 26826*x^4 + 1404627*x^5 +...

such that

1 = 1*(1-x)^3 + 3*x*(1-2^2*x+x^2)^3 + 33*x^2*(1-3^2*x+3^2*x^2-x^3)^3 + 739*x^3*(1-4^2*x+6^2*x^2-4^2*x^3+x^4)^3 + 26826*x^4*(1-5^2*x+10^2*x^2-10^2*x^3+5^2*x^4-x^5)^3 + 1404627*x^5*(1-6^2*x+15^2*x^2-20^2*x^3+15^2*x^4-6^2*x^5+x^6)^3 +...

PROG

(PARI) {a(n)=if(n==0, 1, -polcoeff(sum(m=0, n-1, a(m)*x^m*sum(k=0, m+1, binomial(m+1, k)^2 * (-x)^k )^3 +x*O(x^n)), n))}

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

CROSSREFS

Cf. A212370, A247031.

Sequence in context: A326328 A233319 A003715 * A009690 A229513 A210833

Adjacent sequences: A247027 A247028 A247029 * A247031 A247032 A247033

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 09 2014

STATUS

approved