A067622 Consider the power series (x + 1)^(1/3) = 1 + x/3-x^2/9 + 5x^3/81 + ...; sequence gives numerators of coefficients.

1, 1, -1, 5, -10, 22, -154, 374, -935, 21505, -55913, 147407, -1179256, 3174920, -8617640, 70664648, -194327782, 537259162, -13431479050, 37466757350, -104906920580, 884215473460, -2491879970660, 7042269482300, -59859290599550

Offset

0,4

Comments

a(n) is also the numerator of the binomial coefficient C(k,n) evaluated at k=1/3, e.g. a(4) = (1/24)k(k-1)(k-2)(k-3), plug in k=1/3 and take numerator. - James R. Buddenhagen, Aug 16 2014

Links

Table of n, a(n) for n=0..24.

Formula

a(n) =(-1)^n*A004990(n)*A067623(n)/A000244(n); ignoring signs, a(n) =A038502(A004990(n)) =A038502(A034164(n-2)). a(n)'s sign is (-1)^(n+1) if n>0.

Maple

s := convert(taylor((x+1)^(1/3), x, 50), polynom): for n from 0 to 50 do printf(`%a, `, abs(numer(coeff(s, x, n)))) od;
seq(numer(subs(k=1/3, expand(binomial(k, n)))), n=0..50) # James R. Buddenhagen, Aug 16 2014

Crossrefs

Denominators are A067623.

Sequence in context: A064694 A264147 A229440 * A362284 A196240 A341638

Adjacent sequences: A067619 A067620 A067621 * A067623 A067624 A067625

Keyword

sign,frac

Author

Benoit Cloitre, Feb 02 2002

Extensions

Edited by Henry Bottomley and James A. Sellers, Feb 11 2002

Status

approved