A093541 - OEIS

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A093541

Square array, read by antidiagonals, where column (k+1) equals the self-convolution of row k, with row 0 and column 0 consisting of all 1's.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 12, 6, 1, 1, 5, 28, 33, 8, 1, 1, 6, 56, 138, 72, 10, 1, 1, 7, 100, 486, 500, 137, 12, 1, 1, 8, 164, 1498, 2888, 1532, 236, 14, 1, 1, 9, 252, 4111, 14792, 13772, 4196, 377, 16, 1, 1, 10, 368, 10210, 67692, 110856, 57560, 10518, 568 (list; table; graph; refs; listen; history; internal format)

	OFFSET	`0,5`
	COMMENTS	`Antidiagonal sums form A093542. Main diagonal is A093543.`
	FORMULA	`T(n, k) = sum_{i=0..n} T(k-1, i)*T(k-1, n-i), with T(n, 0)=T(0, k)=1 for n>=0, k>0.`
	EXAMPLE	`Column 2: {1,4,12,28,56,100,...} equals the self-convolution of row 1: {1,2,4,6,8,10,...}.` `Rows begin:` `[1,1,1,1,1,1,1,1,1,1,1,1,1,...],` `[1,2,4,6,8,10,12,14,16,18,20,22,...],` `[1,3,12,33,72,137,236,377,568,817,...],` `[1,4,28,138,500,1532,4196,10518,...],` `[1,5,56,486,2888,13772,57560,219834,...],` `[1,6,100,1498,14792,110856,698816,...],` `[1,7,164,4111,67692,812492,7930308,...],` `[1,8,252,10210,278396,5364868,...],` `[1,9,368,23288,1040856,31939300,...],` `[1,10,516,49394,3581120,173226000,...],...`
	PROG	`(PARI) T(n, k)=if(n<0\|k<0, 0, if(n==0\|k==0, 1, sum(i=0, n, T(k-1, i)*T(k-1, n-i))))`
	CROSSREFS	`Cf. A093542, A093543.` `Sequence in context: A111669 A124834 A104495 * A171881 A160449 A089940` `Adjacent sequences: A093538 A093539 A093540 * A093542 A093543 A093544`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Mar 30 2004`

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Last modified February 16 09:27 EST 2012. Contains 205904 sequences.