A089974 - OEIS

This site is supported by donations to The OEIS Foundation.

A089974

(n+1)-st term of the n-th binomial transform of this sequence equals 1 for all n>=0.

1, 0, -3, 1, 17, -49, -71, 1079, -3263, -10529, 156401, -624601, -1858319, 42109055, -249633047, -187690049, 17346988289, -159631097281, 375894263521, 890514087458, 3, -137481700309199, 830604602372959, 3549053339380121, -139582700722475473, 1526848956867592513 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Equals row sums of triangle A089962, which is the matrix inverse of triangle A071207.`
	FORMULA	`a(n) = sum_{k=0..n} (-1)^(n-k)C(n, k)nk^(n-k-1). 1 = sum_{k=0..n} C(n, k)n^(n-k)a(k). O.g.f.: A(x) = (1-x)sum_{n>=0} x^n/(1+nx)^(n+2). E.g.f.: (1-x)exp(x*exp(-x)).`
	EXAMPLE	`Note the diagonal of 1's in the array of iterated binomial transforms:` `[1, 0, -3, 1, 17, -49, -71, 1079,..]` `[1, 1, -2, -7, 4, 17, -134, 121,..]` `[1, 2, 1, -9, -31, -47, -135, -599,..]` `[1, 3, 6, 1, -52, -271, -1034, -3895,..]` `[1, 4, 13, 29, 1, -445, -3311, -18461,..]` `[1, 5, 22, 81, 212, 1, -5166, -49631,..]` `[1, 6, 33, 163, 689, 2117, 1, -75019,..]` `[1, 7, 46, 281, 1564, 7553, 26830, 1,..]`
	PROG	`(PARI) a(n)=if(n<0, 0, if(n==0, 1, sum(k=0, n, (-1)^(n-k)binomial(n, k)n*k^(n-k-1) )))`
	CROSSREFS	`Cf. A089962, A089981, A071207.` `Sequence in context: A188645 A060281 A151918 * A143849 A105626 A071210` `Adjacent sequences: A089971 A089972 A089973 * A089975 A089976 A089977`
	KEYWORD	`sign`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Nov 18 2003`

Content is available under The OEIS End-User License Agreement .

Last modified February 17 12:38 EST 2012. Contains 206021 sequences.