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A187638 A convolution of binomial coefficients. 1
1, 1, 1, 8, 77, 824, 9448, 113728, 1419349, 18215576, 239034104, 3194168768, 43331889928, 595375647424, 8270102936896, 115966112244224, 1639592525879333, 23350785267093848, 334714889445506584, 4825695011761675456, 69936530485677013528 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 9/8 - (1/8)*(K(16*x)/Pi)^2, where K(x) is the elliptic integral of the first kind (as defined in Mathematica).

a(n) = (1/8)*sum(C(2k,k)^2/(2k-1)*C(2n-2k,n-k)^2/(2n-2k-1), k=0..n) for n >= 1.

Recurrence: n^3*a(n) = 8*(4*n^3 - 12*n^2 + 10*n - 3)*a(n-1) - 256*(n-3)*(n-2)*(n-1)*a(n-2). - Vaclav Kotesovec, Apr 06 2014

a(n) ~ 4^(2*n-1)/(Pi^2*n^2). - Vaclav Kotesovec, Apr 06 2014

MAPLE

seq((-1/8)*add(binomial(2*k, k)^2/(2*k-1)*binomial(2*(n-k), n-k)^2/(2*(n-k)-1), k=0..n), n=1..12);

MATHEMATICA

Table[-1/8 Sum[Binomial[2k, k]^2/(2k-1) Binomial[2n-2k, n-k]^2/(2n-2k-1), {k, 0, n}], {n, 1, 20}]

PROG

(Maxima) makelist((-1/8)*sum(binomial(2*k, k)^2/(2*k-1)*binomial(2*(n-k), n-k)^2/(2*(n-k)-1), k, 0, n), n, 1, 12);

CROSSREFS

Cf. A057718.

Sequence in context: A091686 A091691 A024103 * A092661 A196071 A304303

Adjacent sequences:  A187635 A187636 A187637 * A187639 A187640 A187641

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Mar 12 2011

STATUS

approved

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Last modified October 15 17:45 EDT 2021. Contains 348033 sequences. (Running on oeis4.)