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A184889 a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3). 2
1, 30, 5850, 1644500, 542685000, 196017822000, 75031266310000, 29905319000700000, 12279871614662437500, 5159062111690898125000, 2207046771381366217875000, 958150139674902210123750000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184890(n) where A184890(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+2)*(5k+3).

EXAMPLE

G.f.: A(x) = 1 + 30*x + 5850*x^2 + 1644500*x^3 +...

A(x)^2 = 1 + 60*x + 12600*x^2 + 3640000*x^3 +...+ A184890(n)*x^n +...

MATHEMATICA

FullSimplify[Table[500^n * Gamma[n+1/5] * Gamma[n+3/10] / (Gamma[n+1]^2 * Gamma[1/5] * Gamma[3/10]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)

Join[{1}, With[{nn=15}, Table[5^n/(n!)^2, {n, nn}] Rest[FoldList[Times, 1, Table[ (10k+2)(10k+3), {k, 0, nn-1}]]]]] (* Harvey P. Dale, Sep 20 2014 *)

PROG

(PARI) {a(n)=(5^n/n!^2)*prod(k=0, n-1, (10*k+2)*(10*k+3))}

CROSSREFS

Cf. A184890, A184891.

Sequence in context: A321427 A050984 A169686 * A300147 A087216 A239925

Adjacent sequences:  A184886 A184887 A184888 * A184890 A184891 A184892

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 25 2011

STATUS

approved

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Last modified May 8 11:30 EDT 2021. Contains 343666 sequences. (Running on oeis4.)