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A086619 Product of first n terms of the binomial transform of the Catalan numbers (A007317). 8
1, 2, 10, 150, 7650, 1438200, 1051324200, 3101406390000, 37945707181650000, 1966422437567466300000, 438887790263120370963300000, 427664112802721593716655529100000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)