A027347 Number of partitions of n into distinct odd parts, the least being congruent to 1 mod 4.

1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 5, 6, 6, 5, 7, 9, 8, 8, 11, 12, 12, 12, 15, 18, 17, 18, 22, 25, 25, 26, 30, 34, 34, 36, 42, 47, 48, 50, 57, 64, 65, 69, 78, 85, 89, 93, 104, 114, 118, 125, 139, 151, 157, 166, 183, 198, 207, 219, 240

Offset

1,9

Links

Table of n, a(n) for n=1..68.

Formula

From Peter Bala, Jan 31 2021: (Start)

G.f.: A(q) = Sum_{n >= 0} q^(4*n+1) * Product_{k >= 2*n+1} 1 + q^(2*k+1).

A(q) = Limit_{N -> oo} Sum_{n = 0..2*N+1} (-1)^n * Product_{k = n..2*N+1} 1 + q^(2*k+1) = Limit_{N -> oo} Sum_{n = 0..2*N+1} (-1)^n * Product_{k >= n} 1 + q^(2*k+1). (End)

Maple

G := add( q^(4*n+1)*mul( 1 + q^(2*k+1), k = 2*n+1..50 ), n = 0..25 ):
S := series(G, q, 101):
seq(coeff(S, q, j), j = 1..100); # Peter Bala, Jan 31 2021

Crossrefs

Cf. A026832.

Sequence in context: A177962 A246552 A161091 * A352131 A035438 A029260

Adjacent sequences: A027344 A027345 A027346 * A027348 A027349 A027350

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved