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A304787 Expansion of Product_{k>=1} (1 + x^k)^(binomial(2*k,k)/(k+1)). 0
1, 1, 2, 7, 20, 67, 222, 758, 2617, 9189, 32554, 116494, 420046, 1525221, 5571065, 20457808, 75476447, 279636977, 1039965746, 3880891892, 14527657602, 54537434161, 205270200229, 774460385687, 2928429307876, 11095878177649, 42122749335654, 160192845018335, 610224764470011 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Catalan Number

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A000108(k).

MATHEMATICA

nmax = 28; CoefficientList[Series[Product[(1 + x^k)^CatalanNumber[k], {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d CatalanNumber[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 28}]

CROSSREFS

Cf. A000108, A052805, A052854, A088327, A292668.

Sequence in context: A192680 A000150 A318232 * A115117 A029890 A095268

Adjacent sequences:  A304784 A304785 A304786 * A304788 A304789 A304790

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 18 2018

STATUS

approved

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)