A201953 - OEIS

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A201953

A diagonal of irregular triangle A201949.

1, 3, 15, 90, 629, 5019, 45030, 448776, 4919321, 58825415, 762089899, 10633219662, 158974192987, 2535484008225, 42970371055268, 771162539117408, 14609924404202130, 291386317037291622, 6102681801481066642, 133910606028043519500, 3072216586896101950757 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`G.f. of row n in triangle A201949 equals Product_{k=0..n-1} (1 + k*x + x^2).`
	LINKS	`Table of n, a(n) for n=0..20.`
	FORMULA	`a(n) = [x^n] Product_{k=0..n+1} (1 + k*x + x^2).`
	EXAMPLE	`Triangle A201949 begins:` `[1],` `[1, 0, 1],` `[(1), 1, 2, 1, 1],` `[1,(3), 5, 6, 5, 3, 1],` `[1, 6, (15), 24, 28, 24, 15, 6, 1],` `[1, 10, 40, (90), 139, 160, 139, 90, 40, 10, 1],` `[1, 15, 91, 300, (629), 945, 1078, 945, 629, 300, 91, 15, 1], ...` `where coefficients in parenthesis form the initial terms of this sequence.`
	PROG	`(PARI) {a(n)=polcoeff(prod(j=0, n+1, 1+j*x+x^2), n)}`
	CROSSREFS	`Cf. A201949, A201950, A201951, A201952.` `Sequence in context: A173695 A025748 A097188 * A185369 A024339 A034954` `Adjacent sequences: A201950 A201951 A201952 * A201954 A201955 A201956`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna, Dec 06 2011`
	STATUS	`approved`

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Last modified May 18 13:38 EDT 2013. Contains 225419 sequences.