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A258472 Number of partitions of n into two sorts of parts having exactly 2 parts of the second sort. 2
1, 4, 11, 24, 49, 89, 158, 262, 428, 667, 1033, 1542, 2289, 3313, 4765, 6717, 9427, 13011, 17882, 24260, 32763, 43775, 58268, 76837, 100953, 131629, 171003, 220683, 283877, 363016, 462794, 587005, 742332, 934536, 1173293, 1467022, 1829538, 2273365, 2817858 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = A094533(n)/2. - Vladimir Reshetnikov, Nov 21 2016

MAPLE

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

      `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*

       binomial(j, t), t=0..min(2, j)), j=0..n/i))), x, 3)

    end:

a:= n-> coeff(b(n$2), x, 2):

seq(a(n), n=2..40);

MATHEMATICA

((Log[1 - x]^2 - Log[1 - x] Log[x] + QPolyGamma[1, x] (2 Log[1 - x] - Log[x] + QPolyGamma[1, x]) + QPolyGamma[1, 1, x])/(2 QPochhammer[x] Log[x]^2) + O[x]^45)[[3]] // Simplify (* Vladimir Reshetnikov, Nov 21 2016 *)

Table[SeriesCoefficient[1/QPochhammer[q + x, q], {x, 0, 2}, {q, 0, n}], {n, 0, 40}] // Simplify (* Vladimir Reshetnikov, Nov 22 2016 *)

CROSSREFS

Column k=2 of A256193.

Cf. A094533.

Sequence in context: A290707 A260057 A260150 * A007678 A159350 A159348

Adjacent sequences:  A258469 A258470 A258471 * A258473 A258474 A258475

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 31 2015

STATUS

approved

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Last modified October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)