A061261 - OEIS

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A061261

Limits of diagonals in triangle defined in A061260.

1, 2, 6, 15, 37, 85, 194, 423, 912, 1917, 3974, 8096, 16302, 32382, 63668, 123851, 238756, 456190, 864821, 1627016, 3039845, 5641884, 10406924, 19083836, 34802782, 63135539, 113965033, 204739662, 366156396, 652001918, 1156200929 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Terms 1, 2, 6, 15, 37, 85, ... are limits of diagonals in the triangle T(n, k)=A061260: 1 2, 1 3, 2, 1, 5, 6, 2, 1, 7, 11, 6, 2, 1, 11, 23, 15, 6, 2, 1, 15, 40, 32, 15, 6, 2, 1, 22, 73, 67, 37, 15, 6, 2, 1, 30, 120, 134, 79, 37, 15, 6, 2, 1, 42, 202, 255, 172, 85, 37, 15, 6, 2, 1, 56, 320, 470, 348, 187, 85, 37, 15, 6, 2, 1`
	LINKS	`Table of n, a(n) for n=1..31.`
	FORMULA	`G.f.: Product_{k = 1..infinity} (1 - x^k)^( - numbpart(k + 1)), where numbpart(k) = number of partitions of k, cf. A000041. a(n) = 1/nSum_{k = 1..n} b(k)a(n - k), n>0, a(0) = 1, where b(k) = Sum_{d\|k} d*numbpart(d + 1).`
	CROSSREFS	`Cf. A061260.` `Sequence in context: A017923 A018018 A030009 * A098790 A018019 A034518` `Adjacent sequences: A061258 A061259 A061260 * A061262 A061263 A061264`
	KEYWORD	`easy,nonn,changed`
	AUTHOR	`Vladeta Jovovic, Apr 23 2001`
	STATUS	`approved`

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Last modified May 23 16:56 EDT 2013. Contains 225610 sequences.