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 A342178 Product of first n central Delannoy numbers. 0
 1, 3, 39, 2457, 788697, 1327377051, 11931792311439, 580350446236081521, 154215943727867706493809, 225550533306461376412704772467, 1826384842574005591817185497927226551, 82272644789290466599017454496002856892236169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Eric Weisstein's World of Mathematics, Delannoy Number. FORMULA a(n) = Product_{k=1..n} A001850(k). a(n) ~ c * (1 + sqrt(2))^(n*(n+2)) * exp(n/2) / (2^((5*n+1)/4) * Pi^(n/2 + 1/4) * n^((n+1)/2 - 3/(16*sqrt(2)))), where c = 0.9486848745280397752870611535632702994491680306036912732565033220352175749... MAPLE b:= proc(n) option remember; `if`(n<1, 1,       (3*(2*n-1)*b(n-1) -(n-1)*b(n-2))/n)     end: a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end: seq(a(n), n=0..15);  # Alois P. Heinz, Mar 04 2021 MATHEMATICA Table[Product[Hypergeometric2F1[-k, k+1, 1, -1], {k, 1, n}], {n, 0, 15}] FoldList[Times, 1, Table[Hypergeometric2F1[-n, n + 1, 1, -1], {n, 1, 15}]] PROG (PARI) D(n) = sum(k=0, n, binomial(n, k)*binomial(n+k, k)); \\ A001850 a(n) = prod(k=0, n, D(k)); \\ Michel Marcus, Mar 04 2021 CROSSREFS Cf. A001850, A342170, A342177. Sequence in context: A210925 A300046 A267624 * A342166 A188410 A188388 Adjacent sequences:  A342175 A342176 A342177 * A342179 A342180 A342181 KEYWORD nonn AUTHOR Vaclav Kotesovec, Mar 04 2021 STATUS approved

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)