A349737 a(n) is the common difference of the increasing arithmetic progression C(m,k), C(m,k+1), C(m,k+2) when C(m,k) = A349736(n).

14, 1001, 326876, 463991880, 2789279908316, 69923143311577493, 7237577480931700810180, 3072423560706808979836029648, 5323553660882471719158839565113262, 37516291344074264662783594047461175379710, 124094883176124104767115229835643366860919133861769398480

Offset: 1

Author

Bernard Schott, Nov 28 2021

Keywords

• nonn

Comments

For further information, see A349736.

Examples

			For n = 1, row 7 of Pascal's triangle is 1, 7, 21, 35, 35, 21, 7, 1; C(7,1) = 7, C(7,2) = 21 and C(7,3) = 35 form an arithmetic progression with common difference = 14, hence a(3) = 14.
For n = 2, row 14 is 1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1; C(14,4) = 1001 , C(14,5) = 2002 and C(14,6) = 3003 form an arithmetic progression with common difference = 1001, hence a(4) = 1001.
		

Crossrefs

Cf. A007318, A349736.

Programs

Maple

Sequence = seq((2/n)*binomial(n^2+4*n+2,(n^2+3*n-2)/2), n=1..16);

Mathematica

nterms=15; Table[2/n*Binomial[n^2+4n+2, (n^2+3n-2)/2], {n, nterms}]  (* Paolo Xausa, Nov 29 2021 *)

Formula

a(n) = (2/n) * binomial(n^2+4n+2,(n^2+3n-2)/2) = (2/n) * A349476(n) for n >= 1.

a(n) ~ c*2^(n^2+4*n)/n^2, where c = 8*sqrt(2/(Pi*e)). - Stefano Spezia, Nov 29 2021