A086619 Product of first n terms of the binomial transform of the Catalan numbers (A007317).

1, 2, 10, 150, 7650, 1438200, 1051324200, 3101406390000, 37945707181650000, 1966422437567466300000, 438887790263120370963300000, 427664112802721593716655529100000

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..56

Formula

Determinant of the n X n matrix in the upper left corner of square table A086620.

a(n) ~ c * 5^(n*(n+4)/2) * exp(3*n/2) / (2^(3*n) * Pi^(n/2) * n^(3*n/2 + 27/16)), where c = 0.286457028871544332017553737430712054187435533562040177617845850168... - Vaclav Kotesovec, Oct 27 2017

Mathematica

Table[Product[Sum[Binomial[m, k]*Binomial[2*k, k]/(k+1), {k, 0, m}], {m, 0, n}], {n, 0, 12}] (* Vaclav Kotesovec, Oct 27 2017 *)
Table[Product[Hypergeometric2F1[1/2, -k, 2, -4], {k, 0, n}], {n, 0, 12}] (* Vaclav Kotesovec, Oct 27 2017 *)

Crossrefs

Cf. A007317, A003046, A086620.

Sequence in context: A213457 A060595 A303440 * A294373 A194026 A165940

Adjacent sequences: A086616 A086617 A086618 * A086620 A086621 A086622

Keyword

nonn

Author

Paul D. Hanna, Jul 24 2003

Status

approved