A088466 a(n)=(1/2)*4^n*(2*GAMMA(n + 1/2)^2*hypergeom([n + 1/2, n + 1/2], [1/2, 1/2, 3/2], 1/4) + Pi*n!^2*hypergeom([n + 1, n + 1], [1, 3/2, 2], 1/4))/exp(1)/Pi.

2, 43, 2215, 204236, 29238991, 5968183657, 1640535644378, 582894501073075, 259553822858233471, 141383455055328055916, 92397970113863259277807, 71298681895041458302600993, 64098926090734144410361983410

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Formula

Special values of a sum of two hypergeometric functions of type 2F3.

From Vaclav Kotesovec, Jul 05 2018: (Start)

Recurrence: (1024*n^5 - 14592*n^4 + 81984*n^3 - 226816*n^2 + 308685*n - 165149)*a(n) = (16384*n^7 - 270336*n^6 + 1857536*n^5 - 6872576*n^4 + 14746896*n^3 - 18301956*n^2 + 12132739*n - 3306031)*a(n-1) - (98304*n^9 - 2039808*n^8 + 18425856*n^7 - 94961664*n^6 + 307188704*n^5 - 645528016*n^4 + 879083340*n^3 - 745926560*n^2 + 356620843*n - 72896935)*a(n-2) + 8*(n-3)*(n-2)*(32768*n^9 - 720896*n^8 + 6938624*n^7 - 38286336*n^6 + 133198624*n^5 - 302232248*n^4 + 445870962*n^3 - 410792318*n^2 + 213441169*n - 47366190)*a(n-3) - 64*(n-4)^2*(n-3)^3*(n-2)*(2*n - 7)^2*(1024*n^5 - 9472*n^4 + 33856*n^3 - 58176*n^2 + 47757*n - 14864)*a(n-4).

a(n) ~ 2^(2*n - 1) * exp(2*sqrt(2*n) - 2*n - 1/2) * n^(2*n - 1/2). (End)

Mathematica

Table[FullSimplify[2^((2*n) - 1)*(2*Gamma[n + 1/2]^2*HypergeometricPFQ[{n + 1/2, n + 1/2}, {1/2, 1/2, 3/2}, 1/4]/Pi + n!^2*HypergeometricPFQ[{n + 1, n + 1}, {1, 3/2, 2}, 1/4])/E], {n, 1, 15}] (* Vaclav Kotesovec, Jul 05 2018 *)

Crossrefs

Sequence in context: A188683 A119775 A375620 * A357279 A362762 A177490

Adjacent sequences: A088463 A088464 A088465 * A088467 A088468 A088469

Keyword

nonn

Author

Karol A. Penson, Oct 02 2003

Extensions

a(12) corrected by Georg Fischer, Mar 13 2020

Status

approved