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A317913 Expansion of Product_{k>=2} (1 + k*x^k). 1
1, 0, 2, 3, 4, 11, 14, 29, 35, 85, 101, 187, 276, 419, 686, 1042, 1483, 2258, 3517, 4727, 7720, 10582, 15842, 21985, 32744, 45586, 65598, 93940, 131684, 183731, 260977, 357689, 500476, 699225, 946851, 1342110, 1808841, 2495154, 3375385, 4657186, 6224608, 8524443, 11468183, 15428030 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sum of products of terms in all partitions of n into distinct parts >= 2.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to partitions

FORMULA

G.f.: exp(Sum_{j>=1} Sum_{k>=2} (-1)^(j+1)*k^j*x^(j*k)/j).

a(n) + a(n-1) = A022629(n). - Vaclav Kotesovec, Aug 21 2018

EXAMPLE

a(7) = 29 because we have [7], [5, 2], [4, 3] and 7 + 5*2 + 4*3 = 29.

MAPLE

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

      b(n, i-1)+ i*b(n-i, min(n-i, i-1)))

    end:

a:= n-> b(n$2) -`if`(n=0, 0, b(n-1$2)):

seq(a(n), n=0..50);  # Alois P. Heinz, Aug 10 2018

MATHEMATICA

nmax = 43; CoefficientList[Series[Product[(1 + k x^k), {k, 2, nmax}], {x, 0, nmax}], x]

nmax = 43; CoefficientList[Series[Exp[Sum[Sum[(-1)^(j + 1) k^j x^(j k)/j, {k, 2, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x]

CROSSREFS

Cf. A022629, A025147, A298598, A317912.

Sequence in context: A176541 A295721 A171376 * A141704 A061919 A328883

Adjacent sequences:  A317910 A317911 A317912 * A317914 A317915 A317916

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 10 2018

STATUS

approved

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Last modified September 30 10:18 EDT 2020. Contains 337439 sequences. (Running on oeis4.)