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 A174923 A symmetrical triangle sequence:t(n,m)=((n + m + 1)!/(n + 1)!*m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!)) - (((n + 0 + 1)!/(n + 1)!*0!) + ((2*n - 0 + 1)!/(n + 1)!*(n - 0)!)) + 1 0
 1, 1, 1, 1, -32, 1, 1, -1195, -1195, 1, 1, -70554, -72408, -70554, 1, 1, -6531833, -6649664, -6649664, -6531833, 1, 1, -878169592, -889384176, -889565760, -889384176, -878169592, 1, 1, -161902540791, -163440763020, -163459004940 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, -30, -2388, -213514, -26362992, -4424673294, -977604617500, -276059341118418, -97172808944838504, -41757197999307047062,...}. LINKS FORMULA t(n,m)=((n + m + 1)!/(n + 1)!*m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!)) - (((n + 0 + 1)!/(n + 1)!*0!) + ((2*n - 0 + 1)!/(n + 1)!*(n - 0)!)) + 1 EXAMPLE {1}, {1, 1}, {1, -32, 1}, {1, -1195, -1195, 1}, {1, -70554, -72408, -70554, 1}, {1, -6531833, -6649664, -6649664, -6531833, 1}, {1, -878169592, -889384176, -889565760, -889384176, -878169592, 1}, {1, -161902540791, -163440763020, -163459004940, -163459004940, -163440763020, -161902540791, 1}, {1, -39230231039990, -39518230751780, -39520796507280, -39520824520320, -39520796507280, -39518230751780, -39230231039990, 1}, {1, -12093372555263989, -12164016030566136, -12164505889525704, -12164509997063424, -12164509997063424, -12164505889525704, -12164016030566136, -12093372555263989, 1}, {1, -4622513815535615988, -4644508232680242888, -4644630298138508496, -4644631100102535360, -4644631106393241600, -4644631100102535360, -4644630298138508496, -4644508232680242888, -4622513815535615988, 1} MATHEMATICA t[n_, m_] = (((n + m + 1)!/(n + 1)!*m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!)) - ((( n + 0 + 1)!/(n + 1)!*0!) + ((2*n - 0 + 1)!/(n + 1)!*(n - 0)!)) + 1; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A221423 A062543 A086820 * A176341 A134203 A014777 Adjacent sequences:  A174920 A174921 A174922 * A174924 A174925 A174926 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 02 2010 STATUS approved

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Last modified January 23 16:45 EST 2020. Contains 331172 sequences. (Running on oeis4.)