A363255 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + 1!!*x + 3!!*x^2 + 5!!*x^3 + 7!!*x^4 + ...

1, 2, 12, 86, 816, 9126, 122028, 1855802, 32001504, 613558458, 12989299596, 300515004558, 7550646317520, 204680035934550, 5955892801274796, 185157207502788074, 6125200081143892800, 214837212308039658666, 7963817560398871790604, 311101097650387613661510

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Mathematica

A[m_, n_] := A[m, n] = Which[m == 1, (2 n - 1)!!, m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 20]

Crossrefs

Cf. A001147, A305868, A305870, A316084, A363254.

Sequence in context: A208977 A372104 A097237 * A055531 A305209 A290568

Adjacent sequences: A363252 A363253 A363254 * A363256 A363257 A363258

Keyword

nonn

Author

Ilya Gutkovskiy, May 23 2023

Status

approved