A302577
Convolution square root of A186284 multiplied by 2^n.
Original entry on oeis.org
1, 2, 94, 6628, 554246, 50936956, 4971074892, 505747739784, 53048521913478, 5695802803696236, 622942370315360004, 69155891028297395448, 7772714892571857579036, 882718626126348791323992, 101137353917153181195426264, 11676481964194514316750017040
Offset: 0
-
nmax = 20; CoefficientList[Series[Hypergeometric2F1[1/4, 1/4, 1, 64*x]^(1/4), {x, 0, nmax}], x] * 2^Range[0, nmax]
A127776
a(n) = ( (2^n / n!) * Product_{k=0..n-1} (4*k + 1) )^2.
Original entry on oeis.org
1, 4, 100, 3600, 152100, 7033104, 344622096, 17582760000, 924193822500, 49701090010000, 2721631688947600, 151241747739534400, 8507348310348810000, 483459012855561960000, 27715027900230072360000, 1600820011517288979513600, 93072675982122379574532900
Offset: 0
G.f. = 1 + 4*x + 100*x^2 + 3600*x^3 + 152100*x^4 + 7033104*x^5 + ...
- A. Cayley, An Identity, Messenger of Mathematics, 7 (1878), p. 69
-
[1] cat [n le 1 select 4 else (4*(4*n-3)^2*Self(n-1)/ n^2): n in [1..30]]; // Vincenzo Librandi, Aug 26 2016
-
From Michael Somos, Jun 25 2012 (Start)
a[ n_] := If[ n < 0, 0, (Pochhammer[ 1/4, n] 8^n / n!)^2];
a[ n_] := SeriesCoefficient[ Hypergeometric2F1[ 1/4, 1/4, 1, 64 x], {x, 0, n}];
a[ n_] := SeriesCoefficient[ HypergeometricPFQ[ {1/2, 1/2, 1/2}, {1, 1}, 64 x]^(1/2), {x, 0, n}];
(End)
Join[{1}, RecurrenceTable[{a[1] == 4, a[n] == (4 (4 n - 3)^2 a[n-1] / n^2)}, a, {n, 20}]] (* Vincenzo Librandi, Aug 26 2016 *)
-
{a(n) = if( n<0, 0, prod( k=1, n, (8*k - 6) / k)^2)};
-
{a(n) = my(A); if( n<1, n==0, A = x * O(x^n); polcoeff( subst( 1 / agm(1, sqrt(1 - 16*x + A) ), x, serreverse( x*(1 - 16*x) + A )), n))};
-
seq(N) = {
my(a = vector(N)); a[1] = 4;
for (n=2, N, a[n] = 4*(4*n-3)^2*a[n-1]/n^2);
concat(1,a);
};
seq(15) \\ Gheorghe Coserea, Aug 26 2016
Showing 1-2 of 2 results.
Comments