A282207 Expansion of Product_{k>=0} (1 + (2*k + 1)*x^(2*k+1)).

1, 1, 0, 3, 3, 5, 5, 7, 22, 24, 30, 32, 73, 75, 91, 198, 277, 309, 339, 560, 689, 1078, 1126, 1567, 2703, 3396, 3676, 5086, 7046, 8241, 10896, 13072, 19891, 22975, 27922, 41597, 56117, 62459, 77183, 100793, 131846, 161665, 191446, 255225, 311247, 408418, 467460, 599970, 843441

Offset: 0

Author

Ilya Gutkovskiy, Feb 09 2017

Keywords

• nonn

Comments

Sum of products of terms in all partitions of n into distinct odd parts.

Examples

			a(10) = 30 because we have [9, 1], [7, 3], 9*1 = 9, 7*3 = 21 and 9 + 21 = 30.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000700, A022629, A067553.

Programs

Mathematica

nmax = 48; CoefficientList[Series[Product[1 + (2 k + 1) x^(2 k + 1), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=0} (1 + (2*k + 1)*x^(2*k+1)).