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A034256
Expansion of 2 - (1 - 16*x)^(1/4), related to quartic factorial numbers A034176.
2
1, 4, 24, 224, 2464, 29568, 374528, 4922368, 66451968, 915560448, 12817846272, 181780365312, 2605518569472, 37679807004672, 549048616353792, 8052713039855616, 118777517337870336, 1760702021714313216
OFFSET
0,2
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
KEYWORD
easy,nonn
STATUS
approved