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A074141 Sum of products of parts increased by 1 in all partitions of n. 11
1, 2, 7, 18, 50, 118, 301, 684, 1621, 3620, 8193, 17846, 39359, 84198, 181313, 383208, 811546, 1695062, 3546634, 7341288, 15207022, 31261006, 64255264, 131317012, 268336125, 545858260, 1110092387, 2250057282, 4558875555 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Replace each term in A036035 by the number of its divisors; sequence gives sum of terms in n-th group.

This is the sum of the number of submultisets of the multisets with n elements; a part of a partition is a frequency of such an element. - George Beck, Nov 01 2011

LINKS

Table of n, a(n) for n=0..28.

FORMULA

G.f.: 1/Product_{m>0} (1-(m+1)*x^m). Recurrence: a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), where b(k) = Sum_{d divides k} d*(d+1)^(k/d).

EXAMPLE

The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1, the corresponding products when parts are increased by 1 are 5,8,9,12,16 and their sum is a(4) = 50.

MATHEMATICA

Table[Plus @@ Times @@@ (IntegerPartitions[n] + 1), {n, 0, 28}] (* T. D. Noe, Nov 01 2011 *)

CROSSREFS

Cf. A036035, A074139, A074140, A006906.

Sequence in context: A192873 A017925 A030236 * A122931 A094976 A006869

Adjacent sequences:  A074138 A074139 A074140 * A074142 A074143 A074144

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Aug 28 2002

EXTENSIONS

More terms from Alford Arnold, Sep 17 2002. More terms, better description and formulas from Vladeta Jovovic, Vladimir Baltic, Nov 28 2002

STATUS

approved

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Last modified September 2 17:41 EDT 2014. Contains 246363 sequences.