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A027347 Number of partitions of n into distinct odd parts, the least being congruent to 1 mod 4. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A035438 A029260 A205725

Adjacent sequences:  A027344 A027345 A027346 * A027348 A027349 A027350

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)