A034256 Expansion of 2 - (1 - 16*x)^(1/4), related to quartic factorial numbers A034176.

1, 4, 24, 224, 2464, 29568, 374528, 4922368, 66451968, 915560448, 12817846272, 181780365312, 2605518569472, 37679807004672, 549048616353792, 8052713039855616, 118777517337870336, 1760702021714313216

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = 4^n*3*A034176(n-1)/n!, n >= 2, where 3*A034176(n-1)=(4*n-5)(!^4) := product(4*j - 5, j = 2..n);

O.g.f.: A(x) = 2 - (1 - 16*x)^(1/4).

From Peter Bala, Nov 19 2015: (Start)

For n >= 1, a(n) = 1/(sqrt(2)*Pi)*Integrate_{x = 0..16} x^(n-1)*((16 - x)/x)^(1/4).

It appears that sqrt(A(x)) = 1 + 2*x + 10*x^2 + 92*x^3 + 998*x^4 + 11868*x^5 + 149316*x^6 + ... has integer coefficients. (End)

Crossrefs

Cf. A034176.

Equals 4 * A025749(n), n > 0.

Sequence in context: A334602 A183279 A145237 * A179539 A277612 A216857

Adjacent sequences: A034253 A034254 A034255 * A034257 A034258 A034259

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved