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A305869 Expansion of Product_{k>=1} (1 + x^k)^(2*k-1)!!. 3
1, 1, 3, 18, 123, 1098, 11806, 150406, 2218065, 37206485, 699604235, 14572941915, 333037896380, 8283300923765, 222714069807495, 6436292165450693, 198941178161054798, 6548632634238445779, 228705772883364303114, 8446082393596031365629, 328846269698068735291665, 13462627492562640070346824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Weigh transform of A001147.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..404

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Double Factorial

Index entries for sequences related to factorial numbers

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A001147(k).

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

      binomial(doublefactorial(2*i-1), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..23);  # Alois P. Heinz, Jun 13 2018

MATHEMATICA

nmax = 21; CoefficientList[Series[Product[(1 + x^k)^(2 k - 1)!!, {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d (2 d - 1)!!, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 21}]

CROSSREFS

Cf. A001147, A261052, A305867, A305870.

Sequence in context: A074564 A108241 A199421 * A181998 A176277 A289429

Adjacent sequences:  A305866 A305867 A305868 * A305870 A305871 A305872

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 12 2018

STATUS

approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)