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A177970 Array T(n,m) = A177944(2*n,2*m) read by antidiagonals. 1
1, 1, 1, 1, 26, 1, 1, 99, 99, 1, 1, 244, 622, 244, 1, 1, 485, 2300, 2300, 485, 1, 1, 846, 6423, 12000, 6423, 846, 1, 1, 1351, 15001, 45031, 45031, 15001, 1351, 1, 1, 2024, 30924, 136120, 218774, 136120, 30924, 2024, 1, 1, 2889, 58122, 352698, 831384 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Antidiagonal sums are 1, 2, 28, 200, 1112, 5572, 26540, 122768, 556912, 2490188, ... = 4^d*(d+1/2)-2*d(d+1), d > 0.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

T(n,m) = 1/Beta(2*n+1, 2*m+1) - 2*n - 2*m where Beta(a,b) = Gamma(a)*Gamma(b)/(Gamma(a+b) .

EXAMPLE

The table starts in row n=0, column m=0 as:

.1,.....1,......1,......1,.......1,.........1,.........1,.........1,

.1,....26,.....99,....244,.....485,.......846,......1351,......2024,

.1,....99,....622,...2300,....6423,.....15001,.....30924,.....58122,

.1,...244,...2300,..12000,...45031,....136120,....352698,....813940,

.1,...485,...6423,..45031,..218774,....831384,...2645350,...7354688,

.1,...846,..15001,.136120,..831384,...3879856,..14872836,..49031376,

.1,..1351,..30924,.352698,.2645350,..14872836,..67603876,.260757874,

.1,..2024,..58122,.813940,.7354688,..49031376,.260757874,1163381372,

MAPLE

T:= (m, n) -> (2*n+1)*binomial(2*m+1+2*n, 2*m)-2*n-2*m:

seq(seq(T(m, s-m), m=0..s), s=0..10); # Robert Israel, Jul 06 2017

MATHEMATICA

Clear[t, n];

t[n_, m_] = 1/Beta[2*n + 1, 2*m + 1] - 2*n - 2*m;

a = Table[Table[t[n, m], {m, 0, 10}], {n, 0, 10}];

Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];

Flatten[%]

PROG

(Python)

from sympy import binomial

def T(m, n): return (2*n + 1)*binomial(2*m + 1 + 2*n, 2*m) - 2*n - 2*m

for n in range(11): print [T(m, n - m) for m in range(n + 1)] # Indranil Ghosh, Jul 06 2017

CROSSREFS

Sequence in context: A040677 A040676 A225532 * A225483 A183065 A157630

Adjacent sequences:  A177967 A177968 A177969 * A177971 A177972 A177973

KEYWORD

nonn,easy,tabl,look

AUTHOR

Roger L. Bagula, May 16 2010

EXTENSIONS

Definition rewritten with A177944, examples brought into normal form, closed sum formula - The Assoc. Eds. of the OEIS, Nov 03 2010

STATUS

approved

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Last modified February 25 05:01 EST 2020. Contains 332217 sequences. (Running on oeis4.)